The discord was palpable even in the body language. When Mr. Trump greeted Emmanuel Macron, France’s new president, the two leaders, jaws clenched, grabbed each other’s hands in an extended grip that turned Mr. Trump’s knuckles white. When the leaders lined up to pose for the traditional photograph of leaders at NATO headquarters, Mr. Trump appeared to push aside the Montenegrin prime minister, Dusko Markovic, to get to his assigned place in the front.
The split was starkest at NATO headquarters, where Mr. Trump used the dedication of a soaring new building to lecture allies on their financial contributions. Far from robustly reaffirming NATO’s mutual defense commitment in the way that many members hoped he would, Mr. Trump repeated his complaint that the United States was shouldering an unfair burden.
“Twenty-three of the 28 member nations are still not paying what they should be paying and what they’re supposed to be paying for their defense,” Mr. Trump declared, as the leaders shifted uncomfortably behind him, shooting one another sidelong glances.
“This is not fair to the people and taxpayers of the United States,” he added. “And many of these nations owe massive amounts of money from past years and not paying in those past years.”
Standing before a large piece of twisted wreckage from the World Trade Center that will serve as a memorial at the headquarters, Mr. Trump promised to “never forsake the friends that stood by our side” in the aftermath of the Sept. 11 attacks — a pledge that White House officials later said amounted to an affirmation of mutual defense.
But to European allies, Mr. Trump’s words fell far short of an explicit affirmation of NATO’s Article 5 clause, the “one-for-all, all-for-one” principle that has been the foundation of NATO since its establishment 68 years ago, after World War II.
“I think he was stingy with the U.S. commitment and very generous with his criticisms,” said Fabrice Pothier, a former head of policy planning at NATO and a senior associate at Rasmussen Global, a political consulting firm.
White House officials said Mr. Trump’s message on financial contributions had galvanized NATO to confront the issue of financial contributions. At a closed meeting after his speech, they said, the leaders unanimously approved a resolution on burden-sharing and on fighting terrorism.
“To see unanimous support for the two main priorities of the president is a great way to start it off,” said Sean Spicer, the press secretary. “When you have an entire meeting that is focused on the president’s agenda, that shows the power of his message.”
Publicly, though, the other leaders appeared less gratified than bewildered. During a photo-taking session, none of them spoke to Mr. Trump, except for the secretary general of NATO, Jens Stoltenberg. Afterward, several surrounded Chancellor Angela Merkel of Germany, who has emerged as the strongest counterweight to the president.
Earlier in the day, Mr. Trump, a blunt critic of the European Union during his campaign, received a chilly reception from his European counterparts as they began meetings in Brussels.
His first meeting with the Continent’s leaders began with officials from the United States and Europe saying nothing to each other. After being welcomed to Brussels, Mr. Trump said, “Thank you very much,” but he was otherwise silent as he gazed at the cameras across the room.
Donald Tusk, who represents leaders of the bloc’s 28 member states as president of the European Council, made it clear after the morning meeting that there had been several areas of disagreement.
“Some issues remained open like climate and trade,” Mr. Tusk said after the meeting at the European Union’s lavish new headquarters. “And I am not 100 percent sure that we can say today — ‘we’ means Mr. President and myself — that we have a common position, common opinion, about Russia.”
In the talks, Mr. Trump and Mr. Tusk differed over the intentions and policies of President Vladimir V. Putin of Russia, according to a person with direct knowledge of the meeting who spoke on the condition of anonymity because the talks were private. That reflects growing anxiety in Europe over what appear to be Russia’s efforts to meddle in elections here and in the United States.
The subject of Russia did not come up in a broader meeting between American and European officials, said Michael Anton, a spokesman for the National Security Council. But Mr. Anton said he could not speak for a smaller meeting with Mr. Trump, Mr. Tusk and the president of the European Commission, Jean-Claude Juncker.
The White House put a more positive spin on the day, saying the leaders discussed ways to deepen cooperation in fighting the Islamic State and reaffirmed “the strong bond between the United States and Europe, anchored in shared values and longstanding friendship.”
Climate change is another bone of contention, however. European leaders are turning up the pressure on Mr. Trump not to withdraw from the Paris climate accord that was ratified last year.
The campaign began on Wednesday at the Vatican, when Pope Francis gave Mr. Trump a copy of his influential encyclical on protecting the environment, and the Vatican’s secretary of state, Cardinal Pietro Parolin, urged the president not to withdraw from the accord.
Mr. Trump told Vatican officials that he had not made a final decision about the issue and that he was not likely to do so until after a Group of 7 meeting this weekend in Taormina, Italy, according to Secretary of State Rex W. Tillerson. The president’s senior advisers have been deadlocked for months over whether the United States should withdraw
Prime Minister Justin Trudeau of Canada was among those who said he planned to press Mr. Trump on climate change.
“One of the things that we understand in Canada is that investing in clean energy and investing in fighting against climate change is going to help us,” Mr. Trudeau said, citing efforts by governments and businesses to find ways to avoid polluting the planet.
Mr. Trump’s handling of Article 5 epitomizes the gulf between him and other leaders. His steadfast refusal to endorse it as a candidate, and later as president, has raised fears among NATO allies about whether the United States would come to their defense in the event of an attack.
Other American officials have offered reassurances. Mr. Tillerson told reporters traveling on Air Force One this week, “Of course we support Article 5.” But until Mr. Trump speaks those words, leaders of other NATO nations seem bound to remain concerned.
Instead, Mr. Trump criticized the other leaders for not contributing 2 percent of their countries’ gross domestic product to their defense, as they have agreed to do but have often fallen short. He even took a shot at the new headquarters, a vast glass-and-steel edifice that looks like a series of interconnected airplane hangars.
“I never asked once what the new NATO headquarters cost,” Mr. Trump said. “I refuse to do so. But it looks beautiful.”
In 2014, NATO members agreed to increase their defense spending gradually to meet the 2 percent of G.D.P. goal, with 20 percent of that spending on military equipment. Those commitments have not changed, and after flat defense spending in 2015, spending increased last year among non-American alliance members.
The alarm in Europe over Mr. Trump’s presidency has diminished since the days immediately after his election, in part because emissaries like Mr. Tillerson and Vice President Mike Pence have reaffirmed American support for NATO and the European Union.
But Mr. Trump — who once described Brussels as a “hellhole” overrun with radicals — remains an object of deep suspicion in the city. For some of the European leaders, testing Mr. Trump seemed to be as important as finding common ground with him.