By Julian E. Barnes

BRUSSELS—President Donald Trump committed to attending a summit of North Atlantic Treaty Organization leaders in May, NATO said Monday, a meeting that member countries sought after Mr. Trump’s critical comments about the alliance.

The precise date of the NATO summit in Brussels is yet to be set, but officials said it would be in late May, likely immediately before or after the Group of Seven leaders’ meeting in Sicily.

The commitment to attend the summit was made in a phone conversation between Mr. Trump and NATO Secretary-General Jens Stoltenberg on Sunday evening that officials said also covered the alliance’s counterterrorism efforts, military spending in Europe and the war in Ukraine.

As U.S. allies seek to gauge the new president’s foreign-policy priorities, Mr. Trump said Monday he backed NATO, which he characterized as obsolete days before his inauguration last month.

“We strongly support NATO,” Mr. Trump said Monday in remarks at MacDill Air Force Base in Florida. “We only ask that all of the NATO members make their full and proper financial contributions to the NATO alliance, which many of them have not been doing.”

NATO defense ministers, including U.S. Defense Secretary Jim Mattis, will gather in Brussels next week, where the alliance’s counterterrorism work will top the agenda.

Next week’s meeting will focus on what the alliance is doing to fight terrorism and how it can meet the challenge from the Trump administration to expand its efforts, including stepping up its intelligence sharing and bolstering its work with special-operations forces.

Mr. Stoltenberg and other allied officials have long said NATO’s best contribution to fighting terrorism is to train local forces and advise partner countries’ ministries of defense, efforts the alliance is pursuing in 40 countries.

But Mr. Trump has pressured the alliance to do more to fight terrorism. NATO is also looking at other ways it can expand its counterterrorism efforts in conjunction with boosting its special-operations command, Mr. Stoltenberg said in an interview before his call with Mr. Trump.

“Special-operation forces is one element in a wide range of tools NATO has,” he said. Exactly how the headquarters role would shift is still under discussion, he said.

Officials said NATO’s special-operation headquarters could be expanded to take a greater role in training partner nations’ forces. But some Republicans in Washington have said NATO should go further and examine a bigger operational role for the special-operation-forces command.

Mr. Stoltenberg also said NATO’s new intelligence division is looking to better share information on terror threats, including foreign fighters.

“In a more complex world, with new threats and new challenges, we need intelligence even more to understand the different threats we are faced with. And we need to work more closely together,” he said. “We also need better intelligence to address the threats from foreign fighters and terrorism.”

The secretary-general said allies need to share and understand intelligence “in a better way.”

Allies have disagreed on how involved NATO should be in counterterrorism efforts, arguing the threats are best addressed by national governments and law enforcement. But Mr. Stoltenberg says there is a role for the alliance and has been prodding NATO to do more.

“I‘m looking forward to sitting down with the new administration and to discuss with all allies how we can strengthen NATO’s role in the fight against terrorism,” he said.

Following the defense ministerial and the Munich Security Conference, which starts Feb. 17, Mr. Stoltenberg is set to meet with Vice President Mike Pence in Brussels.

Mr. Pence is also likely to meet with senior European Union officials, European officials announced Monday.

Last month Belgian Foreign Minister Didier Reynders said a summit between European leaders and Mr. Trump was critical. “We might have divergent views on issues,” he said. “But we have to see what things we can do together.”

European foreign ministers met in Brussels on Monday to discuss Ukraine and other issues. While Russian sanctions aren’t up for renewal, there was broad agreement in the talks that Europe wasn’t in the mood to loosen them, especially with violence flaring in Ukraine, diplomats said.

Mr. Trump has caused worry in recent comments about Russia, but European diplomats said there may be more continuity in U.S. policy than expected, noting U.N. Ambassador Nikki Haley’s comments last week that sanctions should stay in place.

On Monday, Federica Mogherini, the European Union foreign policy chief, said Europe would maintain its support for Ukraine and the peace process as violence continues. “The situation in the last days is extremely worrisome for us,” she said.

The accounts of Sunday’s call released by the White House and NATO used different language on Ukraine. The White House, echoing language it has used in other recent statements, said Mr. Trump and Mr. Stoltenberg “discussed the potential for a peaceful resolution of the conflict along the Ukrainian border.”

NATO, on the other hand, said the leaders “discussed the uptick in violence in eastern Ukraine, and prospects for a peaceful settlement.”

The alliance statement also noted that Mr. Stoltenberg emphasized the organization’s consistent stance of seeking to balance the defense of Europe with a dialogue between NATO and Russia.