He is widely believed to have won Venezuela’s presidential election, and by a landslide. But on Monday, instead of making preparations for his swearing-in at the palm-lined palace in Caracas, Edmundo González was at the White House meeting with President Biden.

The encounter, a first for the two men, signals Mr. Biden’s desire to present a broad coalition of support for Mr. González, who met with the right-wing president of Argentina, Javier Milei, over the weekend, and will meet with other regional presidents in the coming days.

It is part of an effort by Mr. Biden, in the final days of his administration, to further isolate Nicolás Maduro, Venezuela’s longtime autocratic leader, who claims he won the country’s July election.

“We had a long, fruitful and cordial conversation with President Biden and his team,” Mr. González said at a news conference outside the White House, but he did not provide any details about the topics they discussed.

The Biden administration did not comment immediately.

Pedro Mario Burelli, a veteran Venezuelan political operative and an opponent of Mr. Maduro’s movement, called the visit part of an effort to “freak him out” — to scare Mr. Maduro into believing that the global political tide is increasingly turning against him.

Yet the meeting is unlikely to change the narrative inside Venezuela: Mr. González, 75, was forced to flee the country shortly after millions of Venezuelans voted for him, and he is now living in exile in Spain. Over the weekend, he promised once again that he would return to his country to be sworn in on Friday.

“By any means, I will be there,” Mr. González told reporters during his visit to Argentina, where he and President Milei appeared together on the balcony of presidential palace, clasping hands. Mr. Milei offered his full support for Mr. González.

But many Venezuelans are skeptical that Mr. González will return to his country anytime soon — the government has placed a $100,000 bounty on his head, and he faces likely arrest if he returns.

Mr. González’s most important political backer, María Corina Machado, a conservative former lawmaker who threw her weight behind him after she was barred from running in the presidential election in July, has been in hiding in Venezuela for months. In a recent video message, she continued to encourage the armed forces to defect to her side. That also has not happened.

Instead, Mr. Maduro is expected to be sworn in for another six-year term on Friday, and the real question hanging over the nation is how a second Trump administration, set to take office on Jan. 20, will approach Mr. Maduro.

Mr. Trump’s picks for foreign policy positions — Senator Marco Rubio of Florida, his choice for secretary of state; Representative Mike Waltz of Florida; and Mauricio Claver-Carone among them — have a history of taking a hard line against Mr. Maduro. They favor harsh economic sanctions meant to squeeze the Venezuelan leader economically rather than negotiating with him.

Yet others wonder if Mr. Trump, who has a penchant for deal-making, will instead engage in dialogue with Mr. Maduro. The U.S. president-elect is eager to reduce migration and to push one of Venezuela’s important allies, China, out of the region.

In an effort to gain leverage over Mr. Trump, Mr. Maduro has spent the last few months detaining foreigners inside Venezuela, including several U.S. citizens who are now in his government’s custody.

Such a dialogue could involve a deal in which Mr. Maduro accepts returned migrants — and releases U.S. citizens — in exchange for the United States’ easing up on sanctions that have hobbled his economic power.

Some U.S. oil executives, eager to do business in Venezuela, have been lobbying for that approach.

But Ms. Machado, in a recent interview with The New York Times, argued that Mr. Trump should take the sanctions route, revoking Biden-era licenses that have allow some oil companies to work in Venezuela. Mr. González has been less vocal about what approach he would like the Trump administration to take.

Luz Mely Reyes, a prominent Venezuelan journalist, said that while Mr. Biden’s meeting with Mr. González marked an important moment, “Biden is leaving soon, and we have to see how the government of Donald Trump will act.”

So far, just one Republican official, Senator Rick Scott of Florida, has announced plans to meet with Mr. González during his visit to the United States.

Representatives for Mr. Trump’s transition team did not respond to a request for comment.

Laura Dib, a Venezuela analyst at the Washington Office on Latin America, a human rights advocacy group, said Mr. González needed a stronger show of support from Republicans.

“I am hoping for Rubio to meet with him,” she said.

On Monday Mr. González was also to appear at the Organization of American States in Washington.

Ms. Machado has called for Venezuelans to head to the streets on Thursday to show their support for Mr. González.

And, despite the Maduro government’s threat to arrest her, she has promised to appear in public that day. “The hour has come to act,” she wrote on X on Saturday. “We’ll see each other in the streets.”

Genevieve Glatskycontributed reporting.

The president of Austria on Monday gave Herbert Kickl, the outspoken leader of the Alpine country’s far-right Freedom Party, the task of trying to form a government coalition, three months after the party won the most votes in a general election.

“Mr. Kickl is confident that he can find viable solutions in the context of government negotiations, and he wants this responsibility,” President Alexander Van der Bellen said during a five-minute speech after meeting with Mr. Kickl.

The president’s request starts a process that could make Mr. Kickl, an anti-immigrant firebrand who has vowed to make the country a “fortress,” Austria’s first far-right chancellor later this year.

What led to this?

The Freedom Party finished first in the Sept. 29 election, with nearly 30 percent of the vote, but was well short of a majority. Despite the victory at the ballot box, it initially looked as if the party, founded by ex-Nazis in the 1950s, would not be part of the new government because mainstream parties refused to work with Mr. Kickl, whom they called a danger to democracy.

Karl Nehammer, the chancellor and head of the conservative Austrian People’s Party, which finished in second place with 26.5 percent, was tasked first by President Van der Bellen with trying to form a government. Chancellor Nehammer reached out to the center-left Social Democrats and the upstart Neos party to try to reach an agreement for a coalition government. But they were unable to bridge their differences over core budget issues, and late last week, first Neos, then the Social Democrats pulled out of the talks.

On Saturday, Mr. Nehammer announced he was resigning both as chancellor and party leader. His hastily elected replacement as party leader, Christian Stocker, then announced that — despite promises made during the campaign — the People’s Party, known as the ÖVP, would be open to coalition talks with the Freedom Party.

What is the Freedom Party?

The party was founded not long after World War II by former members of the SS, the Nazi paramilitary police. The party introduces Mr. Kickl using the word “Volkskanzler,” German for people’s chancellor, before campaign speeches, which evokes the rise of German fascism and Adolf Hitler.

It has a history of denigrating migrants in Austria as criminals and welfare sponges. Under a banner of “Fortress Austria,” Mr. Kickl has called for a temporary halt to accepting new asylum seekers and for a law that would ban them from becoming Austrian citizens.

The party is also close to Moscow — it signed a cooperation contract with President Vladimir Putin’s United Russia Party in 2016 — and is against aid to Ukraine to support its defense against Russia’s invasion. It also has opposed sanctions on Russia. Citing the country’s constitutional neutrality, the party is also against Austria joining NATO.

The party has been in the national government five times already, but always as a relatively weak junior partner. Mr. Kickl was the minister of the interior from 2017 until 2019, when a scandal involving one of Mr. Kickl’s predecessors as party leader forced the conservative chancellor at the time to end that coalition. The party has also been in coalition at the state level with the conservatives.

What are the possible outcomes for Austria’s government?

Although the conservatives and the Freedom Party differ on some key points, like their views on Russia’s war in Ukraine, they overlap on many other points. Experts believe a coalition agreement — which lays out a government’s intended program — between the two right-wing parties will be easier to hammer out than the previous attempt with parties from across the political spectrum. Such talks usually take weeks or even months in Austria.

Mr. Kickl has since the election insisted that he should lead the government. Since the Freedom Party has the most seats in the 183-seat Parliament — 57 to 51 for the conservatives — he has a good claim to being named chancellor.

If the parties cannot find common ground, the president would have to call new elections, because no other combination of parties could add up to a majority. A new vote so soon would be extremely rare for Austria.

Why is it important?

Mr. Kickl would become the first far-right chancellor in Austria since the end of World War II. While voters in many European countries have drifted to the right, few leaders have been as outspoken against immigrants and foreigners as he has, which is certain to raise tensions among Austria’s partners in the European Union. (Since becoming Italy’s prime minister in 2022, Giorgia Meloni has distanced herself from her hard-right past, aligning with the Western mainstream on key international issues. By contrast, Prime Minister Victor Orban of Hungary — who visited Vienna last year at the invitation of the Freedom Party — has been at odds with his fellow European Union leaders for years over his right-wing nationalist stances.)

Although Austria only has 9.1 million citizens, its position near the geographical center of the E.U. and its trade relations, especially with Germany, the bloc’s biggest economy, gives the country an outsized importance.

What has the reaction been?

Several hundred people protested in front of the Hofburg, the presidential palace in central Vienna, as Mr. Van der Bellen and Mr. Kickl met on Monday. They held signs that warned about right-wing extremism and chanted, “Never again Volkskanzler.”

Muslim and Jewish groups expressed their concern after the national election in September. Oskar Deutsch, the president of the Jewish Community in Vienna, said then that the success of the Freedom Party felt “threatening” to many in his community.

Eliana Passentin delights in her house, which sits nearly 3,000 feet above sea level in a Jewish settlement in the occupied West Bank, with a view from the Jordan River to the Mediterranean coast. The dining room looks out over ancient Shiloh, the Israelites’ first capital in ancient times.

But Ms. Passentin would feel even better if the area was annexed by Israel.

Some of President-elect Donald J. Trump’s staffing choices have raised hopes among settlers that that could happen. Pete Hegseth, Mr. Trump’s contentious choice for defense secretary, went to ancient Shiloh for an episode of his “Battle in the Holy Land” series on Fox Nation. Mike Huckabee, Mr. Trump’s pick as the next ambassador to Jerusalem, has visited several times over the years and has argued that all of the West Bank belongs to Israel.

Nearly half a million settlers and roughly 2.7 million Palestinians live in the West Bank. The Palestinians, and much of the world, have long envisioned the territory as part of a future independent Palestinian state, alongside Israel, and consider the Jewish settlements to be illegal. After the Oct. 7, 2023, Hamas-led attack on Israel from Gaza, and with the prospect of a more sympathetic administration in Washington, settler leaders say they are confident that a Palestinian state is off the agenda.

They also hope that Israel will extend its sovereignty over parts, or all, of the territory through annexation — a step it has formally avoided since capturing the West Bank from Jordan in the 1967 Middle East war amid opposition from much of the world.

“We want to live our lives in Israel,” Ms. Passentin said, adding, “I believe the new administration will support whatever Israel decides.”

The West Bank has grown increasingly volatile. Israeli settler attacks on Palestinians and their property have risen sharply, while Israel has carried out a series of deadly raids and drone strikes targeting armed Palestinian militants that have chewed up streets and left many Palestinian civilians in fear.

Nearly 1,000 Palestinians have been killed in the West Bank since the beginning of 2023, according to the United Nations. The Israeli authorities say that most were armed fighters, but at least some were uninvolved civilians. About 50 Israelis were killed by Palestinian assailants in the West Bank during the same period, 18 of them members of the security forces, according to U.N. data. Shin Bet, Israel’s internal security agency, said it had thwarted more than a thousand attacks in 2024, including hundreds of shooting attacks.

On Monday, gunmen shot at a civilian bus and cars passing the Palestinian village of Al-Funduq in the northern West Bank, killing at least three Israelis — a police investigator and two women from a nearby settlement — in what the Israeli authorities described as a terrorist attack.

Some settlers express a wariness of Mr. Trump born of experience. He has not articulated clear plans for the region, other than a vague aim of bringing peace. But they nonetheless believe that the new administration will go along with the wishes of Prime Minister Benjamin Netanyahu’s government — the most right-wing in Israel’s history.

“Trump’s team was here, they saw the reality, and for me, that’s a total relief,” said Yisrael Ganz, the head of the Binyamin Regional Council, which governs the settlements around ancient Shiloh, including the adjacent settlement of Shilo. He is also the chairman of the umbrella council representing the rest of the settlements.

Mr. Ganz recently took Doug Burgum, Mr. Trump’s nominee for interior secretary, on a tour in the area. “I see the people he chose,” Mr. Ganz said of the president-elect.

Support for a two-state solution has been waning for years among Israel’s Jewish majority, and since the Oct. 7 attack, many Israelis fear that a Palestinian state would endanger their country. A recent survey found that nearly two-thirds of Jewish Israelis think Palestinians have no right to a state of their own.

But in his public statements, Mr. Ganz has avoided explicitly telling Mr. Trump what to do. To sound less provocative, instead of sovereignty, he uses vaguer terms like “changing the reality” in Judea and Samaria, the biblical names for the West Bank, which the Israeli government considers disputed, not occupied, territory.

During his first term, Mr. Trump showered Israel with diplomatic gifts, including moving the American Embassy to Jerusalem from Tel Aviv and recognizing the contested city as Israel’s capital. Mike Pompeo, then secretary of state, reversed four decades of U.S. policy by stating that settlements did not violate international law. (Secretary of State Antony J. Blinken returned to the traditional U.S. position in 2024, saying the American government considers settlements to be “inconsistent with international law,” in line with most countries.)

Mr. Trump’s administration also floated a peace plan that strongly favored Israel, discarding the longtime goal of granting the Palestinians a viable state with its capital in Jerusalem.

The proposal, which Mr. Trump called the “deal of the century,” called for Israeli annexation of about 30 percent of the West Bank, including its current settlements, and a disjointed Palestinian state with limited sovereignty. It was immediately rejected by Palestinian leaders and many settlers, who preferred continued ambiguity over what they saw as a patchwork of Israeli and Palestinian territory that would leave many settlements as isolated enclaves.

Adding to the settlers’ wariness, the idea of Israeli annexation was abruptly dumped by both Mr. Trump and Israel’s leaders in favor of forging diplomatic relations between Israel and the United Arab Emirates, Bahrain and Morocco, a process known as the Abraham Accords. The Trump administration is expected to try to expand the accords to include Saudi Arabia, which would most likely require some kind of Israeli acceptance of a pathway to Palestinian statehood.

The settlers are far from homogenous. They include secular, middle-class Israelis seeking affordable housing as well as religious ideologues who believe settling the land is part of a Messianic plan ordained by God.

But in the hills around Shilo and the neighboring settlement of Eli in the central West Bank, the mission of Jewish settlement expansion is clear. Alongside official government-approved settlements, outposts have been built in recent decades without official permits. Some have been retroactively authorized by Israel and have come to resemble the more established neighborhoods.

Ms. Passentin, a mother of eight, came to Israel as a child from San Francisco. She and her husband, David, lived for 10 years in a trailer, then in a tent, helping to establish outposts, before settling in Hayovel, a satellite of Eli, parts of which are still unauthorized after years of court battles over the ownership and status of the land.

As the Binyamin Council’s international relations director, she has accompanied some of Mr. Trump’s close circle on tours and hosted Mr. Hegseth in her home.

One immediate request of the Trump administration from settler leaders is to cancel sanctions imposed by the Biden administration on more than 30 individuals and organizations accused of violence against Palestinians and destruction or seizure of Palestinian property.

Settler leaders like Mr. Ganz say they do not condone the violence, some of which is directed at Israeli forces who come to remove illegal settlement structures. But they say that it is a police matter and that it is a fraction of the anti-settler violence perpetrated by Palestinians.

For all of the enthusiasm in settler circles surrounding Mr. Trump’s election, expectations of what he will actually do once in office are tempered.

Citing an adage that marriage is often better the second time around, Aaron Katsof, a winemaker in Esh Kodesh, a hilltop outpost perched above Shilo, between the Palestinian villages of Qusra and Duma, said of a second Trump term: “You don’t come with the lovey-dovey infatuation of high school sweethearts. But you come with a lot more experience and maturity.” Esh Kodesh still lacks Israeli government authorization and permits for permanent housing.

Rivka Amar, 19, who is nine months pregnant, moved in the fall to Alei Ayin, a tiny outpost between Esh Kodesh and Qusra. She and her husband live in a lone quick-build home there, accompanied only by some young men who sleep in a tent, in what was open land.

Ms. Amar had been lunching at the Merlot Cafe in Shilo with her friend Rina Kohen, 18, who lives on a settler farm in the northern West Bank with her brother and 150 head of cattle. The idea, she said, was for a few settlers to control as much land as possible, to keep territory away from Palestinians.

“If I’m not there, my enemy will be there,” Ms. Amar said.

But, she said, she keeps her focus on the tasks at the hand, not on political shifts in Israel or the United States.

“I don’t wake up in the morning thinking of Biden or Trump,” she said, “but of where to graze the goats.”