If anyone doubted that much of the world felt a great sense of relief when Joe Biden became president, a new survey of attitudes in countries around the world confirms as much. But the survey also underscores the degree to which people in other countries have concerns about the health of America’s democracy after Donald Trump’s presidency.

The survey, produced by Pew Research Center, was released just as Biden was beginning his first trip abroad as president with meetings in which reestablishing U.S. leadership among allies and rallying democracies is a major priority.

The survey showed an overnight change in attitudes across 12 countries since the end of Trump’s presidency: Favorable impressions of the United States jumped from 34 percent before Trump left office to 62 percent now. And while 17 percent had said they had confidence “in the U.S. president to do the right thing regarding world affairs” at the end of Trump’s presidency, 75 percent express confidence in the president today.

Biden’s early actions as president have played well. Across the group of 16 nations included in the survey, a median of 89 percent approves of the administration’s decision to rejoin the World Health Organization. A median of 85 percent approves of Biden’s move to reenter the Paris climate accord. Big majorities approve of his idea to organize a summit of democracies, as well as the decision, after some hesitation, to allow more refugees into the United States, a reversal from Trump’s policy.

On personal attributes, Biden, not surprisingly, bests Trump. Not even a fifth of those abroad saw Trump as well qualified to be president, while more than 3 in 4 say that of Biden. Nine in 10 saw Trump as arrogant and 7 in 10 regarded him as dangerous. For Biden, just 13 percent see him as arrogant and 14 percent see him as dangerous.

Perceptions of the United States ebb and flow with changes in administrations. The reaction to Biden’s arrival as president is similar to what happened when Barack Obama succeeded George W. Bush. Bush was highly unpopular, especially in Europe, as a result of the Iraq War, while Obama had become a warmly regarded figure even before he was elected. Next came a sharp drop in perceptions of the United States and its leadership after Trump won the White House. Now Biden is enjoying a burst of approval.

The survey results show that Biden is speaking to a receptive audience in Europe as he attends the Group of Seven meeting in England and then sessions with leaders at NATO and the European Union in Brussels before his summit with Russian President Vladimir Putin on Wednesday in Geneva. His message, that “America is back,” which he has articulated from the first days of his presidency, is something European leaders and their constituents have wanted to hear after years in which Trump questioned the value of transatlantic organizations and multilateral alliances and belittled some of the leaders of America’s closest allies.

That’s the good news for Biden. The not-so-good news from the survey is that despite the confidence that people abroad express about the change in administrations, there are continuing doubts about the strength of American democracy.

The survey found that, across the countries included, a majority of people (56 percent) say the United States is a “somewhat reliable partner,” an equivocation that underscores the doubts that now exist. World opinion is evenly divided on the question of whether the U.S. political system works well, though just 6 percent say it works “very well” and 44 percent say it works “somewhat well.”

More concerning is how people see U.S. democracy. A minority (17 percent) say the United States is a good example for other democracies to follow. Twenty-three percent say this country has never been a good example. The biggest group, 57 percent, says the United States used to be a good example but has not been in recent years.

Biden has multiple objectives this week, among them is to reassert U.S. leadership among the major democracies in a way that provides concrete evidence of his claim that America is back. The decision by the United States to donate 500 million doses of coronavirus vaccines to poorer countries as part of an overall G-7 commitment of 1 billion doses is one such step.

He also wants to show a united front among U.S. allies as he heads to his meeting with Putin, which will be the most closely watched and analyzed event of his trip. Similarly he will be trying to engage others to join in a mutual effort to check a rising China.

Biden has made the promotion of democracy another centerpiece of his trip overseas. Writing in The Washington Post before he left, he said, “This trip is about realizing America’s renewed commitment to our allies and partners, and demonstrating the capacity of democracies to both meet the challenges and deter the threats of this new age.”

He then posed questions that he hopes the week-long trip will begin to answer: “Can democracies come together to deliver real results for our people in a rapidly changing world? Will the democratic alliances and institutions that shaped so much of the last century prove their capacity against modern-day threats and adversaries?”

The Pew survey is a reminder that, however pleased America’s allies are to see a president restate the importance of alliances and international organizations, there remains a nagging question among people in other countries about America’s internal divisions and the state of the U.S. political system. How well Biden deals with those issues at home will be as or more important than what he says abroad.

During the 2020 election, many politicians and analysts overseas expressed reservations about how much the outcome of the November election would say about the future of the United States. While hoping that Biden would defeat Trump, more than one said, in essence, they would wait until the 2024 election to decide whether Trump or Trumpism was still a potent force. They saw America as an inward-looking nation dealing with deep cultural cleavages, a reckoning on race and threats to democratic institutions.

Biden cannot alleviate all these reservations with his first trip abroad, or perhaps with any dealings with world leaders. The answer will come from what happens at home over the next many months, as the fallout from Trump’s presidency continues to spread division and disinformation and Biden works to enact an enormously domestic agenda.

Major decisions on that agenda await Biden upon his return later in the week. The most pressing will be the question of his infrastructure package and whether he can win agreement on a bipartisan package or move ahead on a Democrats-only strategy. His first attempt, through negotiations led by Sen. Shelley Moore Capito (R-W.Va.), collapsed as he was leaving for Europe. Now a broader, bipartisan group of senators has come up with a plan of its own. The White House, while not dismissive, was reserved in response.

Biden has said repeatedly that the United States and other democracies must show that they can deliver for their people better than authoritarian adversaries. That’s the focus of his costly domestic package, only a small portion of it now enacted into law. Meanwhile, the threats and challenges to democracy at home continue, and the rest of the world is waiting to see whether Biden or anyone else can fix what is broken.