Thousands of American Airlines flights over the holiday season are in danger of cancellation because an error in the company’s internal scheduling system gave too many pilots time off, its union said on Wednesday.

American was scrambling to fill the scheduling hole by offering pilots one and a half times their normal pay, said Gregg Overman, a spokesman for the Allied Pilots Association. But the union, which represents more than 15,000 pilots, filed a grievance, saying that the premium pay was not covered by its contract and that the airline couldn’t guarantee payment.

It was not yet clear on Wednesday whether any flights would be canceled or delayed. Mr. Overman said about 15,000 flights from Dec. 17 to the end of the year were affected.

“I’m sorry I can’t offer any guidance other than: Stay tuned,” Mr. Overman said. “And here’s hoping the folks running the airline come to us and are willing to sit down and work through it, because we don’t have a solution at this point.”