But the NATO summit meeting did produce some substantive accomplishments for those who support the alliance’s traditional focus on maintaining security against Russia. The leaders, including Mr. Trump, had signed on to a statement — issued after the first day of the meeting rather than at its conclusion, reducing the chances that the president might change his mind about it — that highlighted agreement on a plan to improve the readiness and mobility of the armed forces across the Continent and progress on issues like cybersecurity. And they agreed on tough language aimed at Moscow, especially regarding Russia’s annexation of Crimea.

But with Mr. Trump scheduled to meet with President Vladimir V. Putin of Russia on Monday — and with the Trump campaign’s ties to Russia the focus of a wide-ranging investigation — the gathering of the leaders was dominated not by discussion over how to address security threats or Mr. Putin’s efforts to divide the West but by wrangling over money.

Rather than projecting unity ahead of the Trump-Putin meeting, the gathering generated nonstop images of division. Intense concern about the corrosive effects of populism and growing authoritarianism in NATO members like Turkey, Hungary and Poland on support for post-World War II institutions and policies received little or no sustained public attention.

In the weeks before the summit meeting, alliance leaders feared that Mr. Trump would try to blow everything up, dealing a truly severe blow to the multilateral world order and to trans-Atlantic deterrence and cohesion.

On Thursday, Mr. Trump dismissed concerns that his relationship with Russia was too cozy, or that his hardball tactics at NATO had played into the hands of Mr. Putin, whom he is to meet in Helsinki, Finland, next week. But after 48 hours of overt conflict with allies — and the second international summit meeting in two months where he has sparred openly with European leaders — he said he looked forward to a positive encounter with the Russian president.

“I hope that we’re going to be able to get along with Russia; I think that we probably will be able to,” Mr. Trump said. “We go into that meeting not looking for so much.”

The White House hastily called the news conference in Brussels amid reports that Mr. Trump had unleashed a tirade during a closed-door morning meeting against member countries he complained were still not spending enough on their militaries. Mr. Trump used the news conference to hail himself, again, as a “stable genius,” saying he deserved “total credit” for pushing the allies to increase their military spending by more than previously agreed to.