Chinese warships that have been sailing south along the eastern coast of Australia gave notice on Friday of their intent to conduct live fire exercises in international waters between Australia and New Zealand, forcing commercial flights to divert and putting the two countries on edge.

The three naval vessels, which include one of the most powerful warships in the Chinese navy’s fleet, were outside Australia’s exclusive economic zone when the drills took place, Prime Minister Anthony Albanese of Australia told reporters.

The ships were first detected in the region last week, according to Australian officials.

While the Chinese vessels appeared to have acted in accordance with international law, the Australian and New Zealand militaries were closely monitoring them, Mr. Albanese said. He said it was not immediately clear what, if any, live fire drills were conducted Friday.

Analysts have said that the unannounced presence of the warships near Australian territorial waters — thousands of miles away from the Chinese mainland — was a show of force.

In Beijing, a spokesman for China’s foreign ministry described the actions of the ships as “far seas exercises.” They were organized by the People’s Liberation Army’s Southern Theater Command, which also oversees the navy’s activities in the South China Sea.

“The drill was carried out in a safe, standard and professional manner in accordance with relevant international law and international practice,” the spokesman, Guo Jiakun, said.

Airservices Australia, which manages air traffic in the region, said in a statement that it had advised airlines and radioed pilots with planned flights to avoid parts of the Tasman Sea “as a precaution.”

Australia’s foreign minister, Penny Wong, said that she was concerned about the lack of “transparency” in relation to the exercises and the notice given Friday, and said she would raise it with her counterpart, Wang Yi. They were scheduled to meet later Friday at the G20 meeting in South Africa.

The ships, a guided missile cruiser, a frigate and a supply vessel, were first detected off Australia’s northeast coast last week. This week, they passed through waters about 150 nautical miles from Sydney, well outside Australia’s territorial waters but inside its exclusive economic zone.

Australian officials have stressed that the Chinese ships have been traversing regional waters legally, but that they were closely monitoring their movements.

Li You contributed research.

As the United States and Russia begin talks to end the war, Moscow is pressing its advantage on the battlefield by closing in on Dnipropetrovsk, one of Ukraine’s largest regions and one with a major industrial base. Russian troops are now less than three miles from the region’s border, and they have been pushing forward in recent days.

Should the Russian Army cross from the eastern Donetsk region into Dnipropetrovsk, it would deal a big blow to morale in Ukraine — marking the fifth region to face partial Russian occupation and expanding Moscow’s control over the war-torn country. It could also complicate Kyiv’s position in territorial negotiations that might arise during peace talks.

The Russian advance has already reshaped the landscape of Dnipropetrovsk’s border area, once a quiet expanse of rolling fields and small villages. Now, trenches and anti-tank ditches line roads where convoys of armored vehicles pass. Tanks are concealed in tree lines. In villages closest to the front, soldiers have taken over buildings damaged by bombing or abandoned by locals.

The Ukrainian backpedaling can be seen in the westward relocation of the aid station where medics of the 33rd Mechanized Brigade treat wounded soldiers. Late last year, they retreated three times in as many months, hauling medical beds and blood banks in trucks with them.

The medics never thought they would be forced to entirely abandon Donetsk, an area where their unit had fought for a year, and retreat over its western boundary into Dnipropetrovsk.

Earlier this year, that became a reality. Now, the medics fear Moscow’s troops will soon follow.

“It always happens this way,” said Lt. Vitalii Voitiuk, head of the brigade’s medical unit. “When medical units start moving into an area, it means the front line isn’t far behind.” He was speaking at his new aid station near the frontline where injured soldiers receive lifesaving care before being sent to a hospital farther behind the lines.

Outside the aid station, the distant rumble of outgoing artillery fire echoed through the night. “That alone tells you the war is getting closer,” said Mr. Voitiuk, a burly 34-year-old.

Civilians, too, are bracing for the fight. Some have already evacuated — including those who fled the war in the east earlier and do not want to be caught in the violence again — while others are making plans to relocate.

“When we read the requests to evacuate people from Dnipropetrovsk, it felt terrifying,” said Bohdan Zahorulko, a worker at East SOS, a Ukrainian nongovernment organization helping internally displaced people. “But it was also a wake-up call about the reality of the fight.”

Russia’s push toward Dnipropetrovsk, an area of more than three million people with major steel mills, builds on six months of rapid advances in Donetsk. Since August, its troops have captured an average of about 180 square miles of territory each month in Ukraine, nearly four times the size of San Francisco, according to the Black Bird Group, a Finland-based research company. Most of those gains were in Donetsk.

In recent weeks, Russia’s advance has slowed. Franz-Stefan Gady, a Vienna-based military expert who recently returned from a research trip in eastern Ukraine, attributed the slowdown to bad weather hindering Russian mechanized assaults and airstrikes. He also noted Ukraine’s effective use of drones to hit troops and armored vehicles.

“But drones can’t hold territory,” said Lt. Col. Vadim Balyuk, commander of the Shkval Special Forces Assault Battalion in Ukraine’s 59th Brigade. Speaking from a small wooden house in the border area, where he monitors live battlefield footage on screens, he said his unit’s job is to do what drones cannot: secure control of villages and clear a path for Ukrainian infantry to move in.

Colonel Balyuk said his unit had recently cleared two settlements of Russian forces, which could have been used to support their push toward Dnipropetrovsk. But he had no illusions that the fight was over. “The enemy is just regrouping now,” he said.

Soldiers returning from the Donetsk front said Ukraine’s biggest battlefield challenge remains unchanged: an enemy whose overwhelming manpower advantage allows for relentless assaults.

Dmytro, a 35-year-old infantryman with a concussion, was evacuated to the 33rd Mechanized Brigade’s aid point one recent night. He described a four-hour trench battle so fierce that he could not lift his head above the parapet to spot attacking Russian troops. But from the incoming fire, he said, he could tell they were advancing in small groups, methodically closing in.

“All the soldiers from my section of the trench were evacuated,” said Dmytro, who declined to give his last name per military rules.

One of the clearest indications of the approaching fighting is a blue and yellow roadside sign marking the entrance to Donetsk from Dnipropetrovsk. Over three years of war, the site has become a symbol of Ukraine’s resistance, with soldiers heading to battle signing and putting up Ukrainian flags around it. But now, with the front line just 12 miles away, the sign has been draped in a large net to protect it from drone strikes.

In Mezhova, a small town in Dnipropetrovsk standing in the path of the Russian advance, the number of soldiers at times appears to outnumber civilians — they queue at the post office and crowd into cafes, and their olive-green pickups line the streets.

The new reality weighs heaviest on refugees who fled the Donetsk region earlier in the war and resettled in Mezhova and nearby settlements. Over the past three years, the population has surged from 14,000 to 21,000 with their arrival.

“For so long, we thought this place was safe,” said Nelia Seimova, who moved to Mezhova in August after escaping Novohrodivka, which is now under Russian occupation. “I had plans — buying a house, getting a job, sending my child to school. A normal life.”

Now, Ms. Seimova, 33, is planning to move again, farther west. She knows from experience not to wait for the town to be hit with regular bombardment. “We’ve been through this before,” she said, tears filling her eyes.

Each day, Mr. Zrazhevsky studies a battlefield map marked with circles indicating which cities are within the range of the bombs as Russian forces advance. For now, Mezhova is safe. “But we understand that if it happens — and it will at some point — we’ll need to take drastic measures,” he said, possibly mandatory evacuations.

Lists from East SOS, the group assisting refugees, show that some Mezhova residents have already started evacuating. On a recent afternoon in Pavlohrad, a city in Dnipropetrovsk where the group has set up a transit center, refugees who had just been evacuated from towns and villages near the Dnipropetrovsk-Donetsk boundary streamed in.

All were bleary-eyed and some had faces streaked with soot from weeks of burning firewood to keep warm after attacks knocked out the power grid. Among them were elderly women bundled in thick woolen scarves, children in puffer coats and their parents in tears, uncertain of what the future would hold.

Some in Ukraine believe the Trump administration’s push for peace talks might freeze the front line, stopping the Russian advance. Mr. Zrazhevsky, the mayor of Mezhova — which means “border line” in Ukrainian — clings to the hope that a cease-fire will spare his town from evacuation and turn it instead into the new “eastern capital of Ukraine.”

Mykhailo Afendikov, 52, who recently fled Komar, a village in Donetsk, after a glide bomb destroyed his home, struck a more somber tone. Even if the Russians do not capture Komar, he said, “Where can I go back to? There’s no house left.”

It has been a rocky few months for Christian Lindner, and for the German political system that he has thrown into chaos.

In November, Mr. Lindner, who was the federal finance minister, effectively toppled Germany’s fragile government in a bid for his political life. He goaded Chancellor Olaf Scholz into expelling him from the ruling coalition.

That set off a snap election. It means that Mr. Lindner is the primary reason the country will select a new parliament on Sunday, at a time of European and global upheaval in the early weeks of the new Trump administration, and not next fall as originally scheduled.

Mr. Lindner’s move was a bid to save his party, which had slumped in the polls, from its association with an unpopular government. He was trying to avoid a temporary death sentence in federal politics. The question is whether it will work.

In the final week of the campaign, Mr. Lindner and his pro-business Free Democrats remain just under 5 percent of nationwide support in most polls. That is a crucial threshold in German politics. Score above 5 percent, and your party gets into parliament. Fall below it, and you are almost certainly out.

And yet — because of how Germany’s political system is structured — Mr. Lindner retains a chance to play a kingmaker role in the formation of the next government. He just needs to scrape together a little more support, somehow.

“He doesn’t have good cards,” said Stefan Merz, a director at Infratest dimap, a polling firm in Berlin. “But it can’t be ruled out.”

Mr. Lindner is an outlier in German politics, where unflashy, stoic characters abound. He is fond of hunting and sports cars, with an aversion to autobahn speed limits.

Mr. Lindner’s campaign declined interview requests from The New York Times. In an interview last fall with the podcast Hotel Matze, shortly before he initiated the end of the governing coalition, he mused about his fans and detractors alike.

“Those who like you say, ‘The last hope of bourgeois politics in Germany, the last free-market economist in politics,’” Mr. Lindner said. Critics, he added, call him a government debt fetishist, a “neoliberal exploiter and misanthropist.”

“I deal with it in a relaxed manner,” he added.

Mr. Lindner’s grandparents were bakers. His parents divorced when he was a young boy. His mother taught him to prioritize financial independence. From a young age, he yearned to move fast.

A video on YouTube captures a television show for young people recorded in 1997 in which an 18-year-old Mr. Lindner, wearing a suit with a monstrous cow-patterned tie, talks about the advertising business he had started with a friend. It earned him enough to buy his first Porsche by the age of 20.

He was also a political prodigy. Mr. Lindner joined the Free Democrats, or F.D.P., a neoliberal party that favors low taxes on business and high earners — and no speed limits on the highway — at age 16. At age 34, he became the youngest chairman in party history, and he brought it back from the political wilderness.

After failing to win 5 percent of the vote in Germany’s 2013 elections, the Free Democrats spent four years out of parliament. Mr. Lindner brought the party back in 2017, though he pulled out of negotiations to join a ruling coalition with Angela Merkel’s conservative Christian Democrats and the liberal Green Party. “It is better not to govern than to govern wrongly,” Mr. Lindner said at the time.

In 2021, Mr. Lindner helped the Free Democrats score 11 percent of the vote, in part by leading a charge against government restrictions on daily life and economic activity. He joined Mr. Scholz’s Social Democrats and the Greens in a so-called “traffic light” coalition. It was always a troubled partnership, but it worsened as Germany’s economy stagnated and the government’s approval ratings sank.

A fissure opened: Mr. Scholz and the Greens wanted to relax a limit on government borrowing — known as the debt brake — in order to juice economic growth. Mr. Lindner refused.

He also saw ominous signs in the polling. All the ruling parties had lost support, but of the three, only the Free Democrats had slipped below 5 percent. His core of support remains “wealthy entrepreneurs in West Germany,” said Marcel Fratzscher, the president of the German Institute for Economic Research.

Mr. Lindner hatched a plan to collapse the government, in hopes of saving his party. Publicly, it began with a leaked document in which he demanded swift changes from the Green Party’s economy minister, Robert Habeck, and Mr. Scholz.

His requests included tax cuts, regulatory relief and the relaxation of some climate goals that he said were pushing energy prices higher. He was daring Mr. Scholz to fire him. On the day after President Trump won another term in the United States, Mr. Scholz obliged, forcing early elections in the process.

Days later, Die Zeit newspaper revealed that Free Democratic leaders had spent weeks preparing to break with the coalition partners, including drafting a script for it. Mr. Lindner never denied the report. He explained that his party simply was seeking an economic turnaround in order “to make Germany successful again.”

In a blistering statement defending his firing, Mr. Scholz said Mr. Lindner cared only for his base electorate and for “the short-term survival of his own party.”

The ensuing political fallout has been shadowed by the opening weeks of Mr. Trump’s administration, including threats of tariffs on European exports and a pullback of America’s military security blanket that has protected Germany since the end of World War II.

Mr. Lindner has tried frantically to pull the Free Democrats above the 5 percent line. In an early bid to grab attention, he posted on the social media platform X that Germany needed more disruptive thinking like the billionaire Elon Musk has. Mr. Musk instead endorsed a different party — the anti-immigrant Alternative for Germany, or AfD — parts of which have been deemed extremist by German intelligence agencies.

Undaunted, Mr. Lindner continues to preach tax cuts and deregulation, to defend Germany’s constitutional curb on government debt, and to slam his former government partners for their management of the economy.

Mainstream parties have said they will not invite the AfD into a government. So Mr. Lindner’s party may still make a possible coalition partner for the poll-leading Christian Democrats and their chancellor candidate, Friedrich Merz. It could be a valuable one if the returns on Sunday are especially fractured.

But for now, Mr. Merz, who was a guest at Mr. Lindner’s wedding, is not tipping his hand.

As Mr. Lindner hovered a point below 5 percent this month, Mr. Merz was asked in an interview with German media about Mr. Lindner’s Free Democrats. “Four percent,” he said, “is four percent too much.”

Israel said on Friday that one of the bodies Hamas handed over as part of the cease-fire deal did not belong to an Israeli woman taken hostage in 2023, as the Palestinian militant group had claimed.

The revelation prompted further alarm over the future of the brittle truce and hostage-for-prisoner swap deal between Hamas and Israel. Hamas acknowledged there may have been a mix-up.

Here’s what we know so far.

Who were the hostages?

Hamas said on Thursday that it had handed over the remains of four hostages: Shiri Bibas, 32; her two children, Ariel, 4, and Kfir Bibas, less than a year old; and Oded Lifshitz, 83. All four were kidnapped from Nir Oz, a village near Gaza that was devastated in Hamas’s surprise attack on Israel on Oct. 7, 2023.

For many Israelis, the Bibas family had become emblematic of the brutality of the Hamas attack. Footage of a terrified Ms. Bibas clutching her two children while being led away by Palestinian gunmen has been seared into the Israeli public consciousness.

Hamas asserted that all four hostages were killed in Israeli airstrikes. But Israel said that three of the four returned on Thursday — which were identified through DNA testing as belonging to Mr. Lifshitz and the two Bibas children — had been murdered by their captors.

Daniel Hagari, the Israeli military spokesman, said the Bibas children’s captors had killed them “with their bare hands.” He said Israel had shared the forensic and intelligence findings with its allies.

But neither Israel nor Hamas had yet presented evidence for public scrutiny.

What happened on Thursday?

Hamas handed four coffins to the International Committee of the Red Cross in a televised ceremony. Each coffin bore the photo of a captive whose body was supposed to be turned over to Israel, including that of Ms. Bibas.

The display was condemned internationally, including by Volker Türk, the United Nations high commissioner for human rights, who called it “abhorrent and cruel.”

Israeli officials brought the remains to the country’s main forensic institute in Tel Aviv, where three were confirmed to be whom Hamas said they were.

But the fourth was an “anonymous, unidentified corpse,” the Israeli military said early Friday, ruling out that the remains were those of Ms. Bibas.

What are Israel and Hamas saying?

Israel has called the failure to return Ms. Bibas’s remains a severe breach of the cease-fire. Prime Minister Benjamin Netanyahu vowed that Hamas “would pay the full price for this cruel and vicious violation.”

Hamas acknowledged in a statement “the possibility of a mistake or a mixing up of corpses” and said it would investigate, calling on Israel to return the body. The group said it was committed to moving forward with the cease-fire agreement.

What’s next?

Israel and Hamas were set for another hostage-for-prisoner exchange on Saturday — one that would free six Israeli hostages held in Gaza for a number of Palestinians jailed by Israel. Although Israeli officials expressed outraged over Ms. Bibas’s fate, they seemed eager for the next swap to go ahead as planned.

On Friday, the Hamas-linked Prisoner Information Office said that more than 600 detainees would be released in exchange. They were to include 50 Palestinian serving life sentences for deadly attacks against Israelis and another 60 serving long sentences, the office said.

The rest include more than 400 other Gazans detained during the war were also to be released, the office said. These Gazans had generally been imprisoned without formal charges and were often held incommunicado for long periods.

It was unclear how that exchange would go ahead given Israel’s accusation that Hamas did not uphold its end of the deal.

Even if the swap on Saturday does go forward, big questions hover over the future of the truce, which paused 15 months of devastating fighting in Gaza that killed tens of thousands of Palestinian civilians and combatants.

The first phase of the cease-fire deal expires in less than two weeks, and Israel and Hamas have yet to agree on terms to extend it to a second phase.

The European Union vowed on Friday to increase security in the Baltic Sea as the Swedish authorities said they were investigating a new cable break, the latest example of damage to underwater infrastructure in the region.

The European Commission, the bloc’s executive arm, said it would take new steps to prevent and detect threats to submarine cables, which carry internet traffic and transmit electricity.

The severing of several undersea cables in the Baltic Sea in recent months has raised concerns that Russia is using the moves to retaliate against NATO countries that have supported Ukraine. Alliance officials have pointed to Russia as a possible culprit, but have said that it is difficult to prove.

“We want to make sure Europe is equipped not only to prevent and detect sabotage to cables, but also to actively deter, repair and respond to any threat to critical infrastructure,” said Henna Virkkunen, the European Union official who announced the initiative. The recent episodes were of “great concern,” she said, adding that the bloc was taking “decisive action” to protect the cables.

The measures, which the bloc said would be rolled out over the next two years, would bolster security and threat-detection in the region, and prioritize funding for new cables. The measures also strengthened enforcement of sanctions and diplomatic measures against what were termed hostile actors and the “shadow fleet.”

NATO has also stepped up its military presence in the area with a new patrol and surveillance operation, called Baltic Sentry, aimed at protecting infrastructure in the sea.

A spokesman for the Swedish police, Mathias Rutegard, declined to comment on the ownership of the latest damaged cable, but it appeared to be the C-Lion1, a major telecommunications line that runs between Finland and Germany, after its Finnish owner, Cinia, said on Friday that it had detected damage. The cable connects the telecommunications networks of Central Europe to the Nordic countries.

The company said in a statement that the damage was minor and that telecommunications were transmitting as normal, but this would be the third time in recent months that the C-Lion1 had been damaged.

It was unclear what had caused the damage. The authorities in Finland said on Friday that they were investigating after the rupture of a sea cable had been discovered two days earlier.

The Swedish police also opened a preliminary investigation, Mr. Rutegard said, because the damage occurred in the country’s Exclusive Economic Zone, an area where Sweden has rights but which is beyond its territorial waters.

Prime Minister Ulf Kristersson of Sweden said on Friday that his government took “all reports of possible damage to infrastructure in the Baltic Sea very seriously.” Such reports, he said, had to be seen in light of the “serious security situation that prevails.”

The Swedish Coast Guard was informed of the cable break on Thursday and was heading to the area off the eastern island of Gotland, Mattias Lindholm, a spokesman for the service, said.

Cinia, which is majority-owned by the Finnish state, said it had asked the Finnish criminal authorities to investigate. Finland’s interior minister, Mari Rantanen, told the Finnish public broadcaster Yle on Friday that the authorities were still waiting for answers, but that “the possibility of an accident is very small.”

Telecommunications using the C-Lion1 cable, which has been in service since 2016, were interrupted in December, Cinia said, a disruption it attributed to a probable cable cut in the Gulf of Finland. Another break that downed services was detected in late November, Cinia said, east of the Swedish island Oland.

The Finnish authorities in December seized an oil tanker suspected of cutting several vital underwater cables and accused it of being part of a Russian “shadow fleet.” Western officials have said they believe Russia has been using such tankers to elude sanctions. Analysts have said that if Russia is also using shadow fleets to sabotage vital infrastructure in Europe, it would be an escalation in Moscow’s conflict with the West.

Sweden, NATO’s newest member, said in January that it was investigating another incidence of damage to an undersea cable running between Sweden and Latvia. The Swedish authorities boarded a cargo ship it suspected of committing “gross sabotage.”

Archaeologists have found a pharaoh’s tomb in an Egyptian valley west of Luxor, Egypt’s ministry of antiquities announced this week, in what officials called the first excavation of a royal tomb since Tutankhamen’s burial chamber was unearthed over a century ago.

The newly identified tomb belonged to Thutmose II, who is believed to have reigned around 1480 B.C. It was “the last missing royal tomb of the 18th Dynasty,” the Egyptian ministry said in a statement.

The excavation was a joint project by Egyptian and British researchers that began in 2022, when the entrance and main corridor of the tomb were found.

The archaeologists at first thought the tomb belonged to a royal consort, because of its location near the burial places of royal wives and that of Hatshepsut, a queen who took the throne for herself after Thutmose II’s death.

The tomb was also in an unlikely place for a king’s burial: beneath two waterfalls and at the bottom of a slope, during the much wetter conditions of the 15th century B.C.

But evidence from within the tomb showed that it had in fact been built for a king, including fragments of alabaster jars naming Thutmose II as the “deceased king,” and inscriptions naming Hatshepsut. Part of the ceiling was still intact, too, showing blue paint with yellow stars on it, which the archaeologists said were only found in king’s tombs.

“Sometimes discoveries are made, but only later does their true significance become clear with additional exploration,” said Peter Der Manuelian, a professor of Egyptology at Harvard who was not involved in the excavation.

He noted a similar case when, a few decades ago, a tomb in the Valley of the Kings turned out to be “larger and more unusual than anyone had previously realized.” It turned out to have been built for the many sons of Ramses II, one of the most powerful pharaohs of ancient Egypt.

Thutmose II, Professor Manuelian said, “lived during a fascinating period of Egyptian history: the imperialistic and cosmopolitan 18th Dynasty.” His reign was perhaps overshadowed by those of his father, his son and his queen, who reigned for nearly 20 years and built a major temple and tomb for herself.

“We’re still trying to understand the ins and outs of this era,” Professor Manuelian said, “and a ‘new’ tomb will doubtless provide us with additional clues.”

Despite the ministry’s assertion that this was the first such discovery since 1922, not everyone will agree: Archaeologists reported finding pharoahs’ tombs in 1940 and in 2014. A member of the recent research team did not immediately respond to questions seeking clarification.

Nonetheless, the secretary general for Egypt’s Supreme Council of Antiquities, Mohamed Ismail Khaled, described the find as one of the most significant in decades. “This is the first time funerary furniture belonging to Thutmose II has been discovered,” he said in a statement.

But unlike Tutankhamen’s tomb, whose chambers were found packed with artifacts during a 1922 excavation, the tomb of Thutmose II had been all but emptied out.

The archaeologists believe that it flooded shortly after the king’s death, and that its contents were moved to another location. (The mummified remains of Thutmose II were found at Deir el-Bahari, a mortuary complex, in the 19th century.)

“Water damage caused severe deterioration, leading to the loss of many original contents, which are believed to have been relocated during ancient times,” according to Mohamed Abdel Badie, the head of the Egyptian side of the archaeological mission.

He said that archaeologists had been able to restore parts of fallen plaster “adorned with intricate designs, including blue inscriptions, yellow star motifs and elements of the Book of Amduat, a key religious text used in royal tombs.”