American Airlines said Wednesday it is seeing a slight improvement in flight delays and cancellations as it resumes negotiations with the union representing its pilots, who rejected a contract offer from parent company AMR Corp. in August.

A federal bankruptcy judge last month ruled in favor of Forth Worth-based AMR in the contract dispute with the pilots. American began rolling out new employment provisions for pilots the following week, and the airline's operational performance began slipping days later. Only 59 percent of American flights arrived on time in September.

Last month also saw nearly 1,400 American flights canceled and more than 21,000 delayed, compared with an average on-time rate of 86 percent for the country's other large airlines, which had a combined total of 966 cancellations and 35,233 delays.

During the last half of September, the percentage of American flights arriving on time at Bush Intercontinental Airport in Houston hovered in the 40th percentile. Also last month, AMR reported it would lay off 53 Houston-based workers.

AMR, which filed for bankruptcy protection in November, blamed the poor operational performance on its 7,500 active pilots who it said were inciting a "slowdown" or "sick out," putting in unnecessary maintenance and sick requests.

The Pilots Association union denied it, pointing to maintenance outsourcing and describing American's planes as "the oldest fleet in the business." It also blames cancellations and delays on understaffing; saying 500 pilots have retired in the last year.

Data from FlightStats.com show improvement in the past week.

"Over the last several days, we have seen modest improvements that we hope are a trend toward returning to normal operations," American spokesman Bruce Hicks said Wednesday when negotiations resumed.

"We're very pleased that we're back at the table," he said. "The fact is, we sincerely apologize to our customers for the disruptions that they have had over the past few weeks. The level of operation at American Airlines recently has been unacceptable to us and to our customers."

Hicks said the airline has reduced flying by about 2 percent for the month of October to free up personnel.

Tom Hoban, a spokesman for the pilots union, said it will seek "an industry-standard contract."

Helane Becker, an analyst with Dahlman Rose, said it's clear American's poor operational performances have hurt revenues. "It would be hard for them not to," Becker said.

In a note to investors Wednesday, JPMorgan airline analyst Jamie Baker said competitor airlines "haven't cited any material influx of American passengers.

"However, if American's operational challenges continue for much longer, they just might."

Darryl Jenkins, an independent airline consultant, said American has a history of high tensions between the company and the pilots, and that they have become out of touch with fliers as they argue.

"Fliers do not care who is right or wrong, they only want to get to their destination," Jenkins said.

In an article in the New York Times on Sunday, novelist Gary Shteyngart bashed American as the world's worst airline. He described, in biting detail, an American flight from Paris to New York that was delayed overnight.

"One passenger told us this was all part of the union's strategy to destroy the airline," Shteyngart wrote.

Analyst Jenkins described other bad press for American, including reports of seats coming loose on at least three American flights, as unrelated to the labor unrest - something that wouldn't necessarily normally get coverage if American weren't under a microscope.

"Very poorly timed," he said.

kiah.collier@chron.com twitter.com/kiahcollier