WASHINGTON — A day after President Trump promised to slash the red tape involved in weapons sales, the administration announced on Thursday a new policy that could vastly expand sales of armed drones, a contentious emblem of the shift toward remotely controlled warfare.

That change, in addition to a newly released update to the policy governing which nations are allowed to buy sophisticated American-made weapons, is intended to accelerate arms sales, a key priority of Mr. Trump.

The president seemed to foreshadow the new policies on Wednesday night, when he said at a news conference with Prime Minister Shinzo Abe of Japan that after allies order weapons from the United States, “we will get it taken care of, and they will get their equipment rapidly.”

“It would be, in some cases, years before orders would take place because of bureaucracy with Department of Defense, State Department,” Mr. Trump said. “We are short-circuiting that. It’s now going to be a matter of days. If they’re our allies, we are going to help them get this very important, great military equipment.”