The union representing American Airlines pilots said Friday that it has reached an agreement to staff flights during the December holidays after a scheduling glitch gave too many pilots vacation at the same time.

The union, which represents some 15,000 pilots at the largest U.S. carrier, had filed a grievance, saying the solution American had put in place violated pilots' contracts because of how it restricted overtime pay.

The pilots' union said it withdrew the grievance after meeting with senior American Airlines management on Friday.

"With this agreement in principle, we anticipate that American Airlines will be able to maintain a full December schedule as planned for its passengers," it said.

American had originally offered pilots 1½ times their hourly pay to work an unassigned flight.