NEW YORK — American Airlines has reached an agreement with its pilots’ union to avoid cancelling thousands of flights during the holiday season.

A scheduling glitch had left thousands of flights without a captain, co-pilot or both between Dec. 17 and Dec. 31 at dozens of airports. The airline and the Allied Pilots Association had disagreed how to overcome the problem.

American said Friday that the two sides “have put that worry to rest to make sure our flights will operate as scheduled.”

The union said it withdrew a grievance after reaching an agreement in principle. Union spokesman Dennis Tajer said details will be released after pilots see the deal.

American, the world’s biggest airline, expects to operate more than 200,000 flights in December.