BRUSSELS—President Donald Trump jolted U.S. allies on Thursday with fresh demands to boost military spending swiftly, prompting some NATO members to worry his critical approach was undermining the alliance.

Mr. Trump said “tremendous progress” was made on boosting defense outlays during a North Atlantic Treaty Organization summit and declared the group “much stronger than it was two days ago.”

Several NATO leaders disputed Mr. Trump’s assertion of new funding pledges but credit him with encouraging commitments for tens of billions of dollars more in military spending since he came to office last year.

“The United States commitment to NATO is very strong, remains very strong,” Mr. Trump said. “I believe in NATO.”

The president’s praise followed a session in which he pressed other allied leaders to raise their military contributions—ticking down a country-by-country list of defense budgets while praising some and criticizing others, according to Foreign Minister Didier Reynders of Belgium.