AP BUSINESS WRITER

SUSAN HIGHTOWER

FORT WORTH, Texas (AP)—The chairman of American Airlines dug his heels in Sunday, turning down a call from striking flight attendants for a presidential mediation board while announcing up to two-thirds of this week’s flights would be canceled.

Speaking on the fourth day of the planned 11-day strike by the Association of Professional Flight Attendants, airline Chairman Robert L. Crandall acknowledged that American fell short in notifying passengers about canceled flights. But he said it has been impossible to know which flight attendants would report for work and thus which flights would be affected.

In hopes of placating thousands of inconvenienced travelers, Crandall said holders of unused, non-refundable tickets could get their money back. In addition to a refund, displaced passengers also will get a $100 voucher toward an American ticket in the coming year.

The strike by the union representing 21,000 flight attendants has cost the airline at least $10 million per day, Crandall said.

The airline plans to concentrate on flights at its main hubs at Dallas, Miami and San Juan, Puerto Rico. The airline will also focus on flights from New York and Los Angeles. American will put passengers on 12 percent of its flights from Chicago, the airline’s second-largest hub, executive vice president Bob Baker said.

At O’Hare on Sunday, as in previous days, few American flights were listed as ‘‘canceled’‘ on airport monitors, but many said ‘‘see agent’‘ for rerouting. The American baggage claim area was a relative dead zone.

‘‘It’s been really slow,’‘ said skycap Lutar Shaw. ‘‘I walked around yesterday half asleep, and I had to buy a book.’‘

Earlier Sunday, union President Denise Hedges said she wrote American Chairman Robert Crandall asking him to join her in asking the National Mediation Board to request the emergency panel.

‘‘With no settlement offer from you in sight and the heavy-traffic holiday period now upon us, we’ve decided to take the initiative and try to end the strike,’‘ Hedges said.

Crandall rejected the offer, saying an emergency mediation board would put the airline’s future in the hands of people under political pressure who have no long-term interest in the company. He added that the mediation board could be expected to split the difference between the two sides’ offers.

‘‘It’s one more case of his being unwilling to negotiate,’‘ Hedges said after Crandall rejected the union’s offer.

The mediation board had been overseeing contract negotiations between American and the union, which broke off due to differences in pay, health benefits, staffing and scheduling.

A Transportation Department official said it was unclear if the strike would qualify for arbitration by a special presidential panel. In the past such panels have only been established in cases where there is a significant disruption to the economy.

It is up to the National Mediation Board, an independent government agency, whether to recommend that the White House establish a presidential panel to help settle the dispute, said the Transportation Department official, who spoke on condition of anonymity.

A presidential emergency board involving the airlines has not been created since the mid-1960s.

The strike, the first by flight attendants at American, is the biggest against a U.S. airline since 1989.

The company and the union have offered differing estimates of the walkout’s impact. The union claims the strike is being honored by at least 95 percent of the flight attendants, while Crandall said by Sunday more than 17 percent had come to work.

Once the strike is over, the flight attendant staff will be cut by 4,000, Crandall said.

Those of the average 200,000 passengers American carries each day bumped by the strike have been competing for a dwindling number of seats on rival airlines. Other carriers were accepting American tickets, but empty seats are harder to find as Thanksgiving approaches.

If a presidential emergency board was created, the union said, strikers would be ordered back to work under their old contract terms, and the board would take 30 days to review the disputed issues and recommend a settlement.

If the parties didn’t agree, a second 30-day ‘‘cooling-off’‘ period would pass before the union could strike again and the company again could impose new contract terms.

On Nov. 1, the company imposed contract terms that included an average 7.8 percent pay raise for each of four years. The union said it needed a larger raise to make up for previous concessions.