• Mr. Trump’s arrival on Wednesday was greeted by thousands of protesters, and activists unfurled a sign saying, “Resist” near the United States Embassy.
If there’s any real drama in Mr. Trump’s visit, besides wondering if he will go off script, it will be his comments when he unveils a 9/11 memorial — a piece of twisted metal from the World Trade Center, which was destroyed in the Sept. 11 attacks — outside NATO’s new building.
(Chancellor Angela Merkel of Germany will unveil a chunk of the Berlin Wall, which came down in 1989, to symbolize how the alliance kept the peace during the Cold War. Potentially awkward: Mrs. Merkel will meet former President Barack Obama before seeing Mr. Trump.)
While Mr. Trump has decided that the alliance isn’t really obsolete, as he once said, he has never publicly committed to Article 5. But he is expected to finally do so on Thursday, White House officials said, since the only time NATO has ever invoked Article 5 was to defend the United States after the 9/11 attacks. More than 1,000 non-American soldiers from NATO countries have died in Afghanistan in the name of Article 5.
But one never knows what Mr. Trump will say, and NATO officials will not breathe easy until Mr. Trump actually utters the words. Of course, the leaders would also like him to say something critical about Russia and its annexation of Crimea, but Mr. Trump has been pretty quiet on that topic, too.
What he has been vocal about is pressing NATO allies to pay what he says is their fair share of the costs of running the alliance. Secretary of State Rex W. Tillerson, traveling with Mr. Trump to Brussels, said the president would have blunt words for the leaders of other NATO nations on that issue.
The Atlantic alliance’s secretary general, Jens Stoltenberg, announced that NATO would join the global coalition that is fighting Islamic State militants, another gesture toward Mr. Trump.
“This will send a strong political message of NATO’s commitment to the fight against terrorism,” Mr. Stoltenberg said. But a message is what it mostly was. The United States, after all, formed the coalition, which it leads and runs out of its military headquarters, without major NATO input, though numerous member nations are also part of the coalition fighting the Islamic State.
NATO has had a small mission in Iraq to train soldiers there and will enhance it, but will much change now that it has agreed to formally join the coalition? Probably not.
Mr. Trump’s formal introduction to the complexities of the European Union began on Thursday with a cordial handshake a walk through a forest of flags.
Met by Mr. Tusk, the president of the European Council, the American president was guided along a red carpet through the newly completed headquarters of the bloc, where each of the 28 member states flies its national flag. (Britain, of course, is negotiating its divorce from the bloc.)
The building, called the Europa, is meant to represent a fresh start for the Union, the organization that Mr. Trump has called into question with his support for Britain’s decision to leave and for populist Eurosceptics like Marine Le Pen, the French leader of the far-right National Front.
Mr. Tusk, a former Polish prime minister and a staunch defender of democracy and openness, met with Mr. Trump and Mr. Juncker for about an hour.
“You know, Mr. President, we have two presidents in the E.U.,” Mr. Tusk said.
Mr. Tusk, who warned this year that Mr. Trump was threatening Europe’s stability, made his priorities for the meeting clear at a prize-giving ceremony the previous evening. It was, Mr. Tusk told his audience, “important to keep our relations with the United States as close as possible and as long as possible — at least for as long as this value remains a priority also on the other side of the Atlantic.”
Mr. Tusk said he would try to convince Mr. Trump “that euroatlantism is primarily cooperation of the free for the sake of freedom; that if we want to prevent the scenario that has already been named by our opponents not so long ago in Munich as the ‘post-West world order,’ we should watch over our legacy of freedom together.”
Mr. Trump then headed to the Belgian residence of the United States ambassador, where he was set to have a working lunch with President Emmanuel Macron of France.
Amid the pomp and ceremony and red carpet unfurled for his arrival, ordinary Belgians gave Mr. Trump a chilly reception, however.
Thousands marched on Wednesday to protest his presence, carrying signs that read, “Solidarity with the women of the whole world,” “No ban, no wall” and “Trump go away.” At one point, #TrumpNotWelcome was the No. 1 trending hashtag on Twitter in Belgium.
And the famous concert hall Ancienne Belgique put up a sign that said, “Don’t duck for Donald.”
Federica Mogherini, the European Union’s foreign policy chief, said at a news conference on Wednesday that she would welcome the same “message of continuity” about trans-Atlantic cooperation that Vice President Pence brought by visiting Brussels in February, soon after Mr. Trump took office.
Mr. Pence’s visit was “a clear sign” of “willingness to work together,” Ms. Mogherini said.
Her comments represent a widely held hope in Brussels that Mr. Trump will avoid bashing the European project in favor of constructive dialogue on global challenges.
Ms. Mogherini, accompanied by Antonio Tajani, the president of the European Parliament, will attend a meeting on Thursday morning along with Mr. Trump, Mr. Tusk and Mr. Juncker.
Ms. Mogherini said she wanted Mr. Trump to discuss carrying out the Paris agreement on climate change, which in the past he has previously threatened to abandon, and investing in multilateral organizations like the United Nations, where the Trump administration wants further funding cuts.
Even if the Trump administration was set on revising American policies, Ms. Mogherini said, it was important to have “an open and constructive dialogue.”
Ahead of the NATO meeting, Mr. Trump met the Belgian prime minister, Charles Michel, on Wednesday and spoke at a news conference in which he denounced those who were behind the bombing attack in Manchester, England, that left 22 people dead, including children, and about 60 others injured.