Flights already in the air were allowed to continue to their destinations, but planes on the ground from coast to coast could not take off. And travelers could do little to get back in the air until the computer system was restored.
American blamed its reservation system, which is used for much more than booking flights. Airlines commonly rely on such systems to track passengers and bags, update flight schedules and gate assignments and file flight plants. The computers also help determine how much fuel to put in an aircraft or which seats should be filled to balance a plane.
The failure caused cascading delays and cancelations nationwide.
American and sister airline American Eagle had canceled 970 flights and delayed at least 1,068 more by early evening Tuesday, according to flight-tracking service FlightAware.com.
The outage began in midmorning and stretched into the afternoon. The systems were fixed by 4:30 p.m., airline spokeswoman Stacey Frantz said.
But even as some flights took off, the airline expected delays and cancellations to persist for the rest of the day.
At airports, customers whose flights were canceled couldn't rebook on a later flight. Passengers already at the airport were stuck in long lines or killed time in gate areas.
"Tensions are high. A lot of people are getting mad. I've seen several yelling at the American agents," said Julie Burch, a business-meeting speaker who was stuck at Dallas-Fort Worth International Airport waiting for a flight to Denver. "Nobody can tell us anything."
Terry Anzur, a TV news consultant from Los Angeles who was also stranded in Dallas, said American Airlines gate employees were doing everything the old-fashioned, manual way because their computers were useless.
"No one at the counter can do anything. They can't check people in," Anzur said. "The airline is at a dead halt."
Theoretically, an airline could manually do the same work as the reservation system for any one flight. But doing it for hundreds of flights isn't practical.
"There was a time when an airline could fly without a reservation system, but those days for the most part are past," said Scott Nason, American's former technology chief and now a consultant.
If their reservation systems go down, "most airlines would be pretty much without the ability to fly more than a very limited number of flights," he added.
Such system crashes are rare in the airline industry but not unheard-of.
During nearly 29 years at American, Nason recalled maybe one failure every few years. While airlines can fix whatever caused the problem last time, "each time it's something different."
Once an opossum chewed through a cable in Tulsa, bringing down the whole system. Another time, a worker in the airline's data center used a metal tool instead of one that was rubber-coated, causing a short circuit that disabled substantial parts of the system, Nason said.
Passengers used social media to flood the airline with complaints. The airline tweeted back that it was working to fix the problem and apologized for the inconvenience.
To make amends, American offered to book people who needed to travel Tuesday on other airlines and pay for the fare difference. For those who wanted to delay their trips, American offered refunds or waivers from the usual fee for changing a reservation.
But for several hours, the airline wasn't able to process changes and refunds because of the computer failure.
American's problems on Tuesday were reminiscent of what United Airlines passengers endured for several days last year. After merging with Continental, United experienced computer glitches in the combined reservation system. On one day in August, 580 United flights were delayed, and its website was shut down for two hours. Another outage in November delayed 636 flights.
The problems prompted an apology from United Continental Holdings Inc. CEO Jeff Smisek, who acknowledged that the airline had frustrated customers and would need to work to win them back.
American's headache occurred as parent company AMR Corp. seeks government approval to merge with US Airways Group Inc. A merger would let American surpass United to become the world's biggest airline.
The combined American-US Airways plans to use the American system that broke down on Tuesday.
Associated Press Airlines Writers Scott Mayerowitz in New York and Joshua Freed in Minneapolis contributed to this report.