Jens Stoltenberg, NATO’s secretary general, spoke before the meetings on Wednesday, acknowledging the external and internal pressures facing the alliance but insisting that it was agile and strong enough to deal with them.

Speaking outside the Grove Hotel in Watford, England, Mr. Stoltenberg laid out an ambitious agenda for the leaders from North American and Europe: the international fight against terrorism, arms control, combating Russia, and, for the first time, the rise of China.

Mr. Stoltenberg said that China’s growing global power offered “both opportunities but also challenges,” citing a buildup in military capabilities as a looming threat.

But one of the biggest issues for NATO is not emerging superpowers outside the alliance, but the deep divisions and disputes within it. Those tensions were on full display on Tuesday during an exchange between President Trump and President Emmanuel Macron of France, who laid out dueling visions for the alliance.

Asked about what he made of earlier comments from Mr. Macron, who said last month that the alliance was suffering from “brain death,” Mr. Stoltenberg vigorously defended the 70-year-old institution.

“That’s not the case,” Mr. Stoltenberg said. “NATO is agile. NATO is active. NATO is adapting. NATO is the most effective alliance in history.”

Mr. Stoltenberg said that differences among the heads of the alliance’s member states were nothing new, citing disputes over the Suez crisis of 1956 and more recently the war in Iraq.

“There’s always been differences,” he said. “What we have proven and what we also show today is NATO is able to overcome these differences.”

— Megan Specia

Widespread anxiety prevailed in the run-up to NATO’s celebration of its 70th anniversary that President Trump, whose criticism of the alliance as obsolete is well-known, would upend the meeting with a surprise demand or an insult of an ally, as he has done before.

But Mr. Trump found himself in the unusual position of defending NATO after an uproar created by President Emmanuel Macron of France, who told The Economist last month that NATO was suffering “brain death” because of what he described as an absence of American leadership under Mr. Trump.

In a meeting on Tuesday morning with NATO’s secretary general, Jens Stoltenberg, Mr. Trump called Mr. Macron’s comments “very insulting” and a “very, very nasty statement essentially to 28 countries.”

Later, in a meeting with Mr. Macron at the American ambassador’s residence in London, the French leader put Mr. Trump on the defensive not only about his vision for NATO, but also about his handling of a military conflict involving Turkey, the quandary about what to do with captured foreign Islamic State fighters in Syria and a trade dispute between France and the United States.

Mr. Macron was unapologetic. In a Twitter posting later, he acknowledged that his comments had provoked reactions, but said that “we need to be clear about the foundations of NATO. Tomorrow, I will defend the interests of France and Europe.”

— Katie Rogers and Annie Karni

President Trump tweets on meeting with Johnson

In past visits, Mr. Trump has made his hosts uncomfortable with no-holds-barred assessments of the state of British politics, and he has both praised Mr. Johnson and disparaged his main opponent, the Labour leader Jeremy Corbyn.

But this time, he has shown a degree of restraint, refraining from commenting, in news conferences or on Twitter, about the election or the competitors.

Mr. Trump, unlike most of his counterparts, did not speak to reporters ahead of the meeting, and appeared to arrive late — a day after Prime Minister Justin Trudeau of Canada was caught on video apparently commiserating with other leaders about the president’s tardiness to events.

A perturbed Mr. Johnson — who, along with Mr. Stoltenberg was greeting each leader individually for a ceremonial handshake in front of the media — asked how long it would take, and gestured to the wall of cameras, saying, “We’re live now.”

“A half an hour? Forty-five minutes?” Mr. Johnson joked.

After a few awkward minutes that saw the two men rocking back and forth on their heels with their hands behind their backs, President Trump finally walked on stage, smiling as he shook their hands.

President Emmanuel Macron of France, on arrival Wednesday, was asked whether he stood by earlier comments about the “brain death” of the alliance and defended the remarks.

“In fact it allowed us to raise some crucial debates,” he said forcefully as he entered the meeting.

“I think it was our responsibility to raise ambiguities that could be harmful, and to tackle a real strategic debate,” he said. “It has started, I am satisfied.”

— Katie Rogers and Megan Specia

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Trump plugs Pompeo — to run for senator from Kansas

Secretary of State Mike Pompeo’s primary role at the meeting of NATO heads of state is to support President Trump. As it happened, Mr. Trump threw a little support to the whisper campaign surrounding a possible run by Mr. Pompeo next year for the United States Senate from Kansas.

Mr. Pompeo, a former congressman from Kansas, has repeatedly said that he would remain at the helm of the State Department as long as Mr. Trump wanted. On Tuesday, the president left the door wide open for Mr. Pompeo to exit.

“He’s a tremendous guy, doing a tremendous job,” Mr. Trump told reporters at Winfield House, the official residence of the United States ambassador to Britain.

With Mr. Pompeo standing nearby, the president continued: “If I thought we were going to lose that seat — because we shouldn’t lose that seat, it’s a great state, it’s a state that I won overwhelmingly, as you know, we shouldn’t lose that state — then I would sit down and talk to Mike.”

Republicans have held both of the Senate seats from Kansas since 1932. But last year’s election of a Democrat governor — a victory delivered by swing voters in Kansas City’s suburbs — coupled with a potentially divisive Republican primary has raised the possibility of a contested Senate race there in 2020. Mr. Pompeo has until June 1 to declare his candidacy.

Mr. Pompeo has otherwise kept a low profile at the NATO events. He did meet on Tuesday with the British foreign secretary, Dominic Raab, for nearly 40 minutes in what American officials described as a discussion about Iran, 5G networks and the potential for a “robust” bilateral trade agreement if Britain leaves the European Union. Mr. Pompeo also expressed his condolences over last week’s fatal stabbings on London Bridge that the authorities have called a terror attack.

Conspicuously absent from the State Department’s description of the meeting was mention of Harry Dunn, a 19-year-old Briton who died in August when his motorbike collided with a car that was believed to be driven by the wife of an American diplomat. Mr. Dunn’s parents are suing the Trump administration, which has so far refused to extradite the suspected driver, Anne Sacoolas, who has claimed diplomatic immunity.

— Lara Jakes