American, which operates more than 3,500 daily flights worldwide, said it saw no evidence that its technical problems were related to recent events in Boston, where bombings at the finish line of the city's marathon on Monday killed three and injured many others.
The problem with the computer systems began in mid-morning and prompted American to ask the US Federal Aviation Administration to ground its flights until 4 p.m. CDT (2100 GMT).
American, a unit of AMR Corp, said its systems were restored as of 3:30 pm CDT (2030 GMT).
"Flights have resumed, but we expect cancellations and delays throughout the remainder of the day," the carrier said in a statement.
In an updated statement the carrier said some cancellations were likely on Wednesday as well, although they would be few in number.
"Flights from our hubs and international flights having been re-started and we will reposition aircraft and crew throughout the evening," it said.
Asked if there was a safety issue involved, FAA Administrator Michael Huerta said American requested the flight halt based on its operational needs. Huerta added he was not aware of any suggestion that American's computer systems had been hacked.
"Not that I'm aware of," Huerta said when asked if American's computer systems had been disabled by a cyber-attack.
Flight tracking service FlightAware said American had canceled 720 flights, including 400 at Dallas/Fort Worth and 200 at Chicago, two of its major hub cities.
At Los Angeles International Airport, another key hub, airline staff began rebooking passengers by early afternoon, airport spokeswoman Nancy S. Castles said.
Mark Duell, vice president of operations at FlightAware, said American hubs at New York's John F. Kennedy and Miami airports would also experience significant delays.
American, based in Fort Worth, Texas, said that it would provide full refunds to travelers whose plans were not flexible and added there would be no charge for changing reservations. The carrier said customers who needed to travel on Tuesday could rebook with American or another airline and it would honor any fare difference.
Other carriers have also had problems with computer reservation systems. Last year, computer outages at United Continental Holdings stranded passengers at airports around the country.
American plans to merge with rival US Airways Group later this year to form the world's biggest air carrier.