Thousands of flights could be canceled.

Credit: Getty Images/Robert Alexander

UPDATED: Thursday, November 30 1:20 p.m. ET

A technical glitch has reportedly left hundreds of December American Airlines flights without scheduled pilots — a mistake that, if left unsolved, could imperil the status of certain routes during one of the year's busiest holiday travel periods.

The Allied Pilots Association, a union that represents thousands of American Airlines pilots, said that the computer system that rejects or approves pilots' time off requests malfunctioned, allowing too many employees to take vacation time during the holidays, Reuters reports. More than 15,000 flights scheduled to take off between Dec. 17 and 31 were originally affected by the error, according to Reuters.

"The airline is a 24/7 op," American Airlines captain Dennis Tajer told CNBC. "The system went from responsibly scheduling everybody to becoming Santa Claus to everyone. The computer said, 'Hey ya'll. You want the days off? You got it.'"

On Thursday, however, American Airlines released a new statement, saying the situation is largely under control.

“Out of the 200,000 flights American will operate in December, only a few hundred are currently unassigned to pilots," the statement reads. "That number of open flights continues to decrease thanks to our pilots who are stepping up to the plate and picking up trips to ensure customers are taken care of. It’s another example of why we are thankful to have such an incredible team. In addition, we have more reserve pilots on hand in December than normal months and they provide us with the ability to fly many of the trips that are currently uncovered. We have not canceled any scheduled flights in December and will continue to work to ensure both our pilots and our customers are cared for.”

The airline is reportedly offering 1.5 times hourly pay to any pilots who are willing to take extra flights in December, an effort to minimize the damage done by the glitch.

Long-distance travel typically jumps by roughly 23% during the December holiday period, according to the U.S. Bureau of Transportation Statistics, with many of those extra travelers opting to fly. Last year, the Economist reported, United States airlines were cumulatively projected to serve 42.5 million customers during the holiday season. Mass cancellations from a major airline like American — which, along with its regional partner American Eagle, operates nearly 7,000 flights a day — could lead to travel chaos at airports across the country.