Some airports used their official Twitter accounts to say their flights were departing, including McCarran International Airport in Las Vegas, Bob Hope Airport and San Diego International Airport.
The computer problems occurred at the Los Angeles air traffic control center, FAA spokesman Ian Gregor said.
He said some flights had been diverted during the order, which had not prevented some flights from landing.
Officials did not say how many flights were affected by the FAA's order, which was made around 2 p.m.
Incoming flights were reportedly being diverted to other airports not affected by the glitch, disrupting travel plans.
Some flights were diverted and the agency issued a nationwide ground stop for those heading into the airspace managed by the center.
Airport officials urged passengers to check with their individual airlines for flight information.