American Airlines has canceled about 2,500 flights since Thursday after a computer glitch disrupted crew scheduling at one of its regional carriers.

The computer problem occurred at Dayton, Ohio-based PSA Airlines, an American Airlines subsidiary that operates about 12 percent of American's 6,700 flights a day.

All PSA flights were canceled on Tuesday morning as the airline "works through schedules, getting aircraft and crews where they need to be to resume operations," American Airlines spokeswoman Katie Cody said in a statement. "PSA will operate a reduced scheduled over the next few days as it restores full service."

The airline has "stabilized" its computer system, which was operating too slowly to schedule crew members in time for flights, Cody said.

The problem is not affecting any of American's other regional carriers or its mainline operations, she added.

American's shares fell 2.2 percent to close at $41.51 on Tuesday, while the NYSE Arca Airline index fell just over 1 percent.