As President Trump was locked in a war of words with the leader of Colombia over the military deportation of migrants, China’s ambassador to Colombia declared that relations between Beijing and Bogotá were at their “best moment” in decades.

Zhu Jingyang, the ambassador, later said that it was a coincidence that he posted his comment on social media last week, a day after Mr. Trump said he would slap tariffs on Colombia. But the public outreach suggested that Beijing saw an opportunity to strengthen its hand in the high-stakes superpower rivalry between China and the United States.

Two weeks into the second Trump administration, Mr. Trump’s aggressive “America First” foreign policy holds both promise and peril for Beijing.

The perils have always been clear: more tariffs, and the risk of a wider trade war. This weekend, Mr. Trump imposed an additional 10 percent tariffs on goods imported from China, saying the tariffs were a response to China’s failure to curb fentanyl exports. He could answer any retaliation from China with even higher levies.

But even as Beijing calculates the impact of the tariffs on China’s weak economy, it is surely also taking stock of the openings that Mr. Trump’s other moves are giving China.

Mr. Trump has alienated U.S. allies and partners like Canada and Mexico by imposing steep tariffs on their exports. He has weakened America’s global authority by cutting foreign aid and withdrawing from the World Health Organization and the Paris Agreement, a U.N. climate pact.

If the second Trump term marks the sunset of Pax Americana, analysts say China will almost certainly use the opportunity to try to reshape the world in its favor. Beijing, which has long accused Washington of using its dominance to contain China’s rise, has tried to drive a wedge between the United States and its allies, including the European Union, Japan and Australia.

“The Chinese are well aware of the damage Trump has done and is doing to U.S. credibility and influence globally. In fact, it is unfolding faster than even Beijing expected,” said Evan S. Medeiros, a professor of Asian studies at Georgetown University who served as an Asia adviser to President Barack Obama.

Mr. Trump’s threats to take the Panama Canal and Greenland, as well as to annex Canada as America’s 51st state could normalize a world order in which might makes right. That is an approach that is familiar to Beijing, even if Chinese officials rhetorically maintain that it will never seek hegemony or expansion.

If the United States strong-arms Panama over its crucial waterway, or forces Denmark to give up the resource-rich territory of Greenland, it sends a signal to China that when it comes to its own claims to the self-governing island of Taiwan and much of the South China Sea, coercion trumps cooperation.

“China was certainly never going to give up Taiwan or the South China Sea, but with President Trump doing what he’s doing, China is even more determined to safeguard its interests there, that’s for sure,” said Henry Huiyao Wang, president of the Center for China and Globalization in Beijing.

Mr. Wang said China has been encouraged by the first two weeks of the new administration despite the tariffs and appointment of hawkish advisers such as Secretary of State Marco Rubio and Michael Waltz, the national security adviser.

Rather than coming out aggressively to confront China, Mr. Trump has presented himself as someone willing to negotiate and potentially cut a deal with Xi Jinping, China’s leader. Mr. Trump has floated the idea of tying tariffs to the fate of TikTok, which he has said should be half-owned by an American company.

Another potential area for deal making is Ukraine. Mr. Trump has said China should help end Russia’s war in the Eastern European country. China, as Russia’s biggest provider of economic and material support, could conceivably pressure President Vladimir V. Putin to come to the negotiation table.

“Trump wants China’s help to end the war in Ukraine,” Mr. Wang said. “China is one of the best partners for him to do that.”

But with so many competing interests, cooperation would be difficult. China has avoided criticizing Russia’s invasion of Ukraine, for example, taking the position that Russia has a right to protect its national security. Ukraine will not accept China as a peace broker because of China’s pro-Russian position, said Shi Yinhong, an international relations professor at Renmin University in Beijing. Mr. Putin, on the other hand, will not want to look subordinate to China, he said, while Mr. Trump has “no real stomach” to see China lauded for playing a significant role.

On the issue of tariffs, Beijing has to decide if it can afford to escalate a trade war with the United States. On Sunday, it vowed to respond to Mr. Trump’s tariffs by filing a case with the World Trade Organization and with countermeasures to be specified later.

Beijing could hit back with tariffs. A more drastic approach would be for China to engage in “supply chain warfare”: halting shipments to the United States of materials and equipment critical to U.S. industry. In early December, China stopped the export to the United States of minerals like antimony and gallium, which are needed to manufacture some semiconductors.

The risk to China is that a trade war would be more damaging to itself than it would be for the United States. Exports, and the construction of factories to make them, are among the few strengths now in China’s economy. As a result, China’s trade surplus — the amount by which its exports exceeded imports — reached almost $1 trillion last year.

China has also not yet said how it will respond to a potentially farther-reaching provision in the fine print of Mr. Trump’s executive order on Saturday: the elimination of duty-free handling for packages worth up to $800 per day for each American. Factories all over China have shifted in recent years to e-commerce shipments directly to American homes, so as to bypass the many tariffs collected on clothing and other goods that are imported and sold through American stores.

In the race for global influence, some argue that the Trump administration’s move to freeze most foreign aid, which has disrupted aid programs around the world, has already benefited China.

In regions like Southeast Asia, where attitudes toward the United States have hardened because of Washington’s support for Israel in the Gaza war, the halt in funding has raised questions about American reliability.

“China needs to do nothing in the meantime, and yet, somehow, net-net, look like the good guy in all of this,” said Jeremy Chan, a senior analyst on China at the Eurasia Group.

Senator Lindsey Graham, Republican of South Carolina, defended the importance of soft power to America’s standing.

“If you don’t get involved in the world and you don’t have programs in Africa, where China is trying to buy the whole continent, we’re making a mistake,” he said last month.

Russia’s full-scale invasion of Ukraine three years ago convinced Europe’s leaders that they needed to spend more money on defense. On Monday, leaders from across the European Union and Britain will meet in Brussels to debate a vexing question: how to pay for it.

It is a concern made more acute by President Trump’s return to the White House.

The United States is the largest military funder of Ukraine’s war effort, but Mr. Trump has suggested he will rapidly withdraw U.S. financial and military support and leave it to the Europeans. He has also insisted that NATO nations ramp up defense outlays to 5 percent of their annual economic output, a drastic increase from the 3 percent or 3.5 percent NATO plans to make its goal at its next summit meeting this summer.

The United States itself spends only about 3.4 percent of gross domestic product on defense.

With the war, the European Union, which was founded on free trade and termed itself a “peace project,” has become more committed to deterrence and defense. It is now scrambling to expand its defense industries and make spending more efficient and collaborative. Prime Minister Keir Starmer of Britain will attend Monday’s gathering, the first time since Britain left the European Union that a British leader has met with the 27 leaders of the bloc in Brussels.

Part of the debate will be whether the European Union will be able to raise more money to pay for defense through common debt, as it did to fight Covid.

But the issue is thorny: Such joint fund-raising might impede the efforts of member countries to meet the individual demands that the NATO alliance is already making of them in terms of raising military budgets. Of the 27 E.U. countries that will meet in the closed-door session on Monday, 23 are members of NATO.

NATO’s supreme allied commander in Europe, Gen. Christopher G. Cavoli, has already set capability targets for the first time since the Cold War. The American general has given NATO member countries specific requirements for equipment and force levels, as well as instructions on how to respond in case of a Russian invasion.

There is consensus among officials and analysts that Europe lacks crucial elements of defense like integrated air and missile defense, long-range precision artillery and missiles, satellites, and air-to-air refueling tankers that only the United States currently provides. Replacing those systems would take Europe at least five or perhaps 10 years, the analysts say.

European nations also want to reduce duplication. Ukraine, for example, has been sent at least 17 different kinds of howitzers, not all of which use the same type of shell.

As Russia threatens from the East and Mr. Trump’s support wavers from the West, Europe’s leaders agree that they need a plan to both coordinate and expand their military resources. But diverging national interests and competing budget priorities mean that reshaping European defense will be difficult, expensive and lengthy.

And important countries on the eastern flank, like Poland and the Baltic nations, want to do whatever they can to keep the United States engaged in NATO and the defense of Europe.

The summit Monday is a first step. The E.U. leaders will discuss military financing and joint procurement, and be joined by Mr. Starmer and by Mark Rutte, the NATO secretary general. The goal is to hash out priorities, which will inform the continent’s top diplomat, Kaja Kallas, and its new defense commissioner, Andrius Kubilius, as they work to draw up a more concrete plan, especially for weapons production.

The meeting also has symbolic importance, defense analysts said, as a demonstration that Europe is taking seriously a long-term threat from Russia and the need to reduce its military dependency on the United States.

“This is critical for Europeans,” said Alexandra de Hoop Scheffer, acting president of the German Marshall Fund, a think tank. “They don’t have a choice, because war is taking place on their own continent.”

Deterring Russia, which wants to split the United States from NATO and divide both the alliance and the European Union, is “a generational struggle,” she said. “But our political leaders have failed to explain to a younger generation why the alliance is important and why it’s important for Ukraine to win this war,” she said.

Europe’s relationship with Washington is also on Monday’s agenda, including how to cope with Mr. Trump’s demands. Officials expect the discussion to address his insistence that he wants to acquire Greenland. The island is an autonomous territory of Denmark, both an E.U. member state and a NATO ally. Danish and Greenlandic leaders say the territory is not for sale and will not be handed over to the United States.

The Greenland issue underscores just how drastically Washington’s relationship to Europe may be changing, as Mr. Trump seems more willing to put economic and military pressure on U.S. allies than on its adversaries.

But there is still a degree of shock in Europe.

“Nobody takes it seriously, or literally,” said Jacob Funk Kirkegaard, a senior fellow at Bruegel, a think tank in Brussels, who studies European economies and trans-Atlantic relations. “Nobody wants to do so, because it would require rethinking the world as we know it.”

While leaders like Mr. Rutte have emphasized that the continent cannot realistically go it alone without the United States, the goal is to be more self-sufficient.

E.U. nations have increased military outlays in recent years. They spent an estimated $340 billion on defense in 2024, a 30 percent increase compared with 2021. At least 23 of NATO’s 32 members now spend 2 percent or more of their gross domestic product on defense, in line with NATO goals. Mr. Rutte has made it clear that 2 percent is a floor, not a ceiling, and that a new, higher standard will be set this year.

With President Vladimir V. Putin of Russia busy with Ukraine and his military battered, European and NATO officials believe there is a window of perhaps three to seven years before Mr. Putin might be tempted to test the NATO alliance.

Finding a fix that boosts and coordinates European defense outlays will not be easy.

“The logic tells us that you need to have joint procurement,” said Janis Emmanouilidis, director of studies at the European Policy Center. But there are barriers, including a lack of trust between nations and conflicting national self-interest. “It is protecting national industry, it is protecting the sovereign right to make decisions,” he said.

When it comes to joint procurement, there is also the issue of how to finance it. Joint funding programs are clearly on the agenda, but exactly what that could look like varies.

It could mean a collective pot of money like Europe raised during the 2020 coronavirus pandemic. Funding could also come from a vehicle supported by the European Investment Bank, which is the lending arm of the European Union, or from a group of nations outside the structures of the bloc.

In a joint letter last week, 19 European countries said the bank “should continue exploring further ways to take an even stronger role in providing investment funding and leveraging private funding for the security and defense sector.”

The letter suggested a serious discussion of “specific and earmarked debt issuance” for defense projects. For now, key member states like Germany and the Netherlands reject the idea of collective borrowing for defense, and the EIB is prohibited from making loans for strictly military uses.

Any serious European defense would have to include Britain, a nuclear power and member of the United Nations Security Council, the main reason Mr. Starmer has been invited to attend. He has himself emphasized security cooperation with the European Union as a way to bring post-Brexit Britain closer to the bloc.

Mark Landler contributed reporting from London.