The problem at the Los Angeles Air Route Traffic Control Center, which handles higher-altitude aircraft, meant planes bound for the region were also grounded.
Around 4:30 p.m., the Los Angeles International Airport reported that flights had resumed. But delays were expected to last several hours.
Government officials were not immediately sure why the system had failed. Areas affected by the shutdown included Southern California, western Arizona, southern Nevada and part of Utah.
The computer that failed is part of the En Route Automation Modernization system, known as ERAM. The F.A.A. has been rolling it out since 2008 in an effort to integrate data from more sources, increasing the number of planes that can be tracked and allowing more direct routing, among other improvements.
The F.A.A. said in a statement that the air traffic center “experienced technical issues” and stopped accepting flights into the airspace for about an hour. Some inbound flights were diverted, the F.A.A. said.
Failures of computers and communications equipment were common in the F.A.A. system through the 1990s and the 2000s but have become much less frequent. Each of the 20 Air Route Traffic Control Centers has two computers running in parallel; if one fails, the other is supposed to kick in. The computers’ tasks include matching radar blips to text blocks that show an airplane’s identity and flight plan.
The F.A.A.’s national air traffic delay webpage showed extensive delays at Los Angeles, Las Vegas and Salt Lake City. By 3:30 p.m., the F.A.A. said gate holds and taxi delays had reached up to 2 hours, 15 minutes.
At Bob Hope Airport, in Burbank, Calif., travelers broke into applause when a Southwest Airlines gate agent announced that flights would resume.
“O.K., everybody, I have good news,” the agent said. “We want to get you out of here. We want to get Phoenix out of here. We want to get everybody out here. We were just released to be able to go.”
Before the announcement, Southwest was advising passengers to book trips for the following day. Most people milled around debating what to do, and whether to wait it out.
Lockheed Martin is the prime contractor for ERAM, which will cost the F.A.A. more than $2.1 billion. The Government Accountability Office said in September 2012 that poor contract oversight had contributed to delays and cost overruns in the program. Deployment got off to a slow start when the system was first installed in Salt Lake City, because of software problems, but air traffic experts said it had been running better recently.