DALLAS (AP) — American Airlines said Thursday that only a few hundred of its late-December flights remain without pilots scheduled to fly the plane and the airline has not canceled any holiday-season flights.

The pilots' union, however, said the staffing shortage caused by scheduling glitch is much more serious.

The Allied Pilots Association said that data from American's scheduling system still showed "thousands" of flights without full crews. The numbers had not changed much from previous days, said union spokesman Dennis Tajer.

The dispute appears to indicate that American is counting heavily on staffing flights with "reserve" pilots. Those are pilots who are scheduled off but agree to be available for fill-in duty.

Airline spokesman Matt Miller said the system viewed by the union does not register flights that American expects to fill with reserve pilots until the day before the flight. He said the airline keeps a larger number of pilots on reserve in December than other months, and it will also use overtime to entice other pilots to work the unstaffed flights.

The pilots' union had said that more than 15,000 flights lacked a captain, co-pilot or both when a problem was discovered in the company's scheduling system. Pilots were allowed to take vacation days in the last two weeks of December even if there wasn't another pilot available to operate the flight.

American has declined to say how many flights were originally affected, but it did not dispute the union's initial figure. The airline has about 15,000 pilots and roughly 200,000 flights scheduled during December.

News of the scheduling glitch had caused some passengers to worry that their holiday flights could be canceled for lack of pilots.

Miller said the number of unassigned flights continues to decrease as pilots pick up additional flying assignments. He declined to say how much the scheduling mix-up and overtime payments will cost Fort Worth, Texas-based American Airlines Group Inc.

American is the world's largest airline.

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David Koenig can be reached at http://twitter.com/airlinewriter