Thousands of December flights on American Airlines do not yet have pilots scheduled to work because of an error in its scheduling system.

A glitch in the system that bids for pilots' time off based on seniority is behind the shortage, the Allied Pilots Association union said.

The union estimated that more than 15,000 flights from December 17-31 - a critical holiday travel period - were affected, according to the Daily Mail.

Flights at some of American Airlines' biggest hubs, including Dallas-Fort Worth, Boston, Miami, New York, Philadelphia, Salt Lake City, Chicago and Charlotte, NC, have been left without pilots.

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"Basically there's a crisis at American for manning the cockpits," said Dennis Tajer, a spokesman for the Allied Pilots Association.

The system error was disclosed to pilots on Friday, the union said.

"We are working through this to make sure we take care of our pilots and get our customers where they need to go over the holiday," American Airlines spokesman Matt Miller said on Wednesday.

Miller also said that American has "reserve pilots to help cover flying in December" but he didn't say how many would be able to cover the flights.

The glitch caused the scheduling system to show that American had enough coverage for some planned flights when it actually didn't.

Miller said the company has made adjustments to the system and expects it to operate smoothly from now on.

As customers got whiff of the issue on Wednesday, some took to social media to ask American what they are doing about the problem.

"We want to keep families flying this holiday season and fully expect to avoid cancellations," American Airlines tweeted to several customers.

In an email sent to employees, American had offered pilots extra pay to work certain flights in the busy holiday period.

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American offered the pilots 150 per cent of their normal hourly wage to pick up some of the flights, the top rate laid out in their contract.

But a grievance filed by the union against management said that the restrictions on overtime pay were a violation of the group's contract.

As of early on Wednesday, the union said management had still not reached out to discuss how best to resolve the shortage.

"I'm watching a 'Grinch that stole Christmas' thing happening. And we don't want to see that happening for our passengers," Tajer said.

Last year, more than 45 million passengers traveled by plane between December 16 through January 5.

Shares of American Airlines Group Inc. lost nearly $2 after news of the glitch, although they still closed up 3 cents at $49.25. Rivals fared much better — Delta, United, Southwest and JetBlue all rose at least 3 per cent.