BRUSSELS—NATO has reached an agreement with holdout France to increase allied funding for counterterrorism programs, clearing a significant obstacle to the Trump administration’s agenda for the alliance.

Under the deal, allied diplomats said, the North Atlantic Treaty Organization will spend an additional $12 million to $24 million on counterterrorism programs next year. The overall NATO budget of roughly $1.6 billion will rise modestly to encompass the new spending.

The French have been forcefully opposed to increasing common funding in recent years, particularly for counterterrorism initiatives, and have expressed concerns about how the money is spent.

Many members don’t see counterterrorism as the alliance’s core mission, but at a NATO meeting of leaders in May there was broad agreement to expand training.