DALLAS — American Airlines said if pilots do not end actions that are disrupting its flights, it will take their union to court.

A top American Airlines executive told union leaders that some pilots were conducting ‘‘an unlawful, concerted effort to damage the company’’ by filing more maintenance complaints and other tactics, leading to a surge in late and canceled flights.

Denise Lynn, the company’s senior vice president of people, asked union officials to denounce any ‘‘work actions.’’ She said the pilots’ actions alienated passengers and threatened the company’s financial prospects just as American parent AMR Corp. is trying to turn itself around after a decade of huge losses.

The union, which is angry over the company’s decision to use bankruptcy protection to impose new pay and work rules on pilots, said Thursday there is no sickout or slowdown causing a spike in canceled and delayed flights.

Allied Pilots Association spokesman Tom Hoban blamed the flight problems on a shortage of pilots and old planes that need frequent maintenance.

American and AMR filed for bankruptcy protection in November and are trying to cut annual spending on labor by $1 billion.