A spokeswoman said all of the airline's flights were affected during the glitch that began about 8 p.m. Pacific time Friday evening.
Because of the hour, however, most of the halted flights were in the west, CNN reported Saturday.
"Flights have started to depart, but employees are working through a manual process so their routine work flow is taking a bit longer," said Michelle Agnew, a spokeswoman for the airline.
"The manual process is involved because the team doesn't have access to all of the normal tools they would use to be able to communicate and dispatch flights," Agnew said.
The Los Angeles Times reported that planes began to take off at 10:30 p.m.
The glitch involved software the airline uses to dispatch flights, the Times said.