WASHINGTON—The Pentagon has launched a wide-ranging push to speed up sales of U.S. arms to foreign allies in an effort to better compete with China and refill the arsenals of friendly nations that have given military gear to Ukraine.

The Pentagon last month created a task force of senior officials to examine longstanding inefficiencies in U.S. sales of billions of dollars of weaponry to foreign countries. The so-called “tiger team” will look at ways for the Defense Department to streamline parts of the program, according to a senior defense official, with the aim of putting coveted American drones, guns, helicopters, tanks and other weaponry into partners’ and allies’ hands faster, officials said.