WASHINGTON—President Donald Trump has given the Central Intelligence Agency secret new authority to conduct drone strikes against suspected terrorists, U.S. officials said, changing the Obama administration’s policy of limiting the spy agency’s paramilitary role and reopening a turf war between the agency and the Pentagon.

The new authority, which hadn’t been previously disclosed, represents a significant departure from a cooperative approach that had become standard practice by the end of former President Barack Obama’s tenure: The CIA used drones and other intelligence resources to locate suspected terrorists and then the military conducted the actual strike. The U.S. drone strike that killed Taliban leader Mullah Mansour in May 2016 in Pakistan was the best example of that hybrid approach, U.S. officials said.

The Obama administration put the military in charge of pulling the trigger to promote transparency and accountability. The CIA, which operates under covert authorities, wasn’t required to disclose the number of suspected terrorists or civilian bystanders it killed in drone strikes. The Pentagon, however, must publicly report most airstrikes.

Mr. Trump has indicated he wants to accelerate the fight against Islamic State and other militant groups. The CIA first used its new authority in late February in a strike on a senior al Qaeda leader in Syria, Abu al-Khayr al-Masri, U.S. officials said. The strike in northern Syria on Mr. Masri, a son-in-law of the late al Qaeda leader Osama bin Laden, had been reported, but it wasn’t previously known that the CIA had carried it out under the new authority. U.S. officials are still assessing results of the strike.

Spokesmen for the Pentagon and the CIA declined to comment.