European leaders plan to use a summit that starts Thursday to agree on a sweeping new strategy to rebuild strained relations with the United States, after four years of a divide-and-conquer approach from President Trump.

From rebuilding the Iran nuclear deal to fighting the pandemic to addressing climate change, Europeans are scrambling to seize the moment with the incoming U.S. leader. Because of Joe Biden’s age and history, many here believe he will be more interested in cooperation with Europe than any U.S. president for the foreseeable future, Democrat or Republican.

But leaders on both sides of the Atlantic warn that some of the irritants of the Trump years will remain, and other divides could still open — especially on what may be the greatest foreign policy challenge of Biden’s presidency, an increasingly aggressive and expansionist Beijing. European countries vary sharply on how they think they should manage relations with China, and the most populous and most powerful country in Europe, Germany, also has the closest trading relationship with Beijing.

European leaders also have become embroiled in an intramural debate about the extent to which they should seek independence from the United States, a goal increasingly pushed by French President Emmanuel Macron and opposed by Germany and others.

“We must be able to act multilaterally when we can. This is our preference,” E.U. foreign policy chief Josep Borrell said this week after European foreign ministers discussed transatlantic strategy at a meeting in Brussels. But Europe must also “be able to act autonomously when we must, in order to promote and defend more effectively our interests and values.”

Trump frequently had Europe in his crosshairs, declaring the European Union his greatest “foe” on trade issues and slapping around Germany and others for defense spending that failed to meet NATO pledges. Unlike President Barack Obama, who declared ahead of Britain’s June 2016 referendum on membership within the European Union that he wanted Britain to remain, Trump stoked Brexit.

“Everyone around the world who wishes to see us divided has been opening bottles of champagne the last few years. That is not okay anymore,” the E.U. ambassador to the United States, Stavros Lambrinidis, said at a panel on transatlantic relations last week.

But though it may be Europe’s turn to pop the bubbly, many policymakers are cautious about how permanent the reprieve from Trumpism may be.

“There’s a sense that this is the last chance,” given the possibility that a Trump ally could recapture the White House in 2024, said Rosa Balfour, the head of the Brussels office of the Carnegie Endowment for International Peace, a think tank.

Many of Biden’s pledges align neatly with E.U. priorities. Already, the European Commission has issued a strategy paper that details a long list of issues it hopes to tackle with the Biden administration.

Europeans want the United States back in the World Health Organization and as a leader in global efforts to combat the pandemic — as Biden has said he would make happen from Day 1. They want Washington to rejoin the Paris climate accord, another first-day plan for the incoming Biden administration. They are laying the groundwork for a revival of the Iran nuclear deal, meeting next week in Vienna to formally invite the United States to rejoin the accord after Trump pulled the plug on U.S. involvement. And they hope Biden will drop Trump’s tariffs on steel and aluminum imports and take a more conciliatory approach to trade issues.

And at NATO, a transatlantic group of strategists released a grand plan last week to overhaul the alliance in the next decade to attune it more toward threats from China, a shift that would bring it more in line with U.S. security preoccupations.

“It’s both wonderful and scary because if we screw up this window, it’ll just be heart-wrenching,” said Anthony Gardner, who was U.S. ambassador to the European Union under Obama and advised the Biden campaign on Europe issues.

But Gardner said that some of the biggest issues — including China — may be thorny, in part because Europe itself remains divided.

“We really should be more aligned on China, but getting between that statement of intent and the actual delivery is going to be hard,” Gardner said.

The continent has become more skeptical of Beijing during Trump’s term, but some countries remain dependent on trade with China even as a growing number have agreed to keep Huawei out of their infrastructure systems, a U.S. priority.

“If Europe can’t solve these differences within, it’s very difficult to propose to the U.S. a proactive plan,” Balfour said.

Biden brings a long history to the relationship with Europe, first with his longtime chairmanship of the Senate Foreign Relations Committee and later as vice president, when he was frequently dispatched around the world to resolve thorny issues of international affairs.

That is good and bad for Europe, given that Trump’s anger that Europe isn’t active enough in global security issues was largely an undiplomatic reformulation of frustrations from the Obama years.

When Biden as vice president met in Rome with Italy’s then-president, Giorgio Napolitano, shortly after the Arab Spring, for instance, he complained that the United States was standing alone against Syrian President Bashar al-Assad as he stoked a bloody war in his country, according to an adviser to Napolitano.

“Biden told Napolitano, ‘We have said what the red lines are in Syria, but we don’t see anyone raising their hands and saying we’re with you,’ ” said Stefano Stefanini, a former Italian diplomat who was Napolitano’s diplomatic counselor at the time.

Stefanini said that although Europe’s engagement with security issues in its neighborhood is still lagging, the bigger irritant may be in its relations with China.

“Europeans have to realize that given the way the ground has shifted between China and the U.S. in the last four years, the idea that exists in some European corners — to continue trading with China as if the rivalry between the U.S. and China is not Europe’s business — cannot apply,” Stefanini said.

European divisions are deep enough that they may struggle to be a strong partner to the United States on all of Washington’s priorities. At the leaders’ summit Thursday and Friday, they will discuss Brexit, their tumultuous relationship with Turkey and their bitter fight with Hungary and Poland about rule-of-law issues.

Relations with Washington will be one of the few areas of concord.

Correction: Stefanini said that although Europe’s engagement with security issues in its neighborhood is still lagging, the bigger irritant may be in its relations with China. An earlier version of this article incorrectly cited Stefanini as saying Russia was the bigger security irritant.