Fort Worth, Texas ? Flight attendants at American Airlines agreed Friday to the wage and benefit concessions that the airline said it needed to avoid bankruptcy.

But the company’s new chief executive, Gerard Arpey, said the world’s largest carrier still has work to do, and he warned that some employees would lose their jobs.

“We are not out of the woods yet,” Arpey said Friday. “Working with our unions and all of our employees, together we will put American Airlines back on top.”

Two of the carrier’s unions had agreed to the company’s concessions request Thursday, but leaders of the Association of Professional Flight Attendants had been split. There also was lingering anger within the union at Donald Carty, who resigned as chairman and chief executive Thursday.

“With new leadership in place at AMR, there was a renewed willingness from management to begin to repair the damage done to relations with its employees,” said John Ward, president of the flight attendants’ union.

The company’s concessions plan shortens the length of employees’ wage and benefit concessions to five years, with limited renegotiations possible sooner, and includes potential bonuses up to 10 percent for employees.

Airline officials had said the carrier would file for Chapter 11 protection unless all three unions accepted.

Employees had voted last week to accept concessions, but then learned that while they were agreeing to cuts, the company had approved bonuses and pension payments for its top executives.

Carty apologized for not disclosing the executive perks, but his relationship with employees was beyond repair, union leaders said.

With the airline’s fate still up in the air and its financial situation deteriorating, Carty resigned after an emergency meeting of parent AMR Corp.’s board Thursday.

AMR Corp. board chairman Edward Brennon, left, applauds as Gerard Arpey, American Airlines chief executive officer, finishes a news conference in Grapevine, Texas. Flight attendants agreed Friday to wage and benefit cuts that the airline said it needed to avoid bankruptcy.

“It is now clear that my continuing on as chairman and CEO of American Airlines is still a barrier that, if removed, could give improved relations — and thus long-term success — the best possible chance,” Carty, 58, said in a statement.

Unions representing American Airlines pilots and ground workers on Thursday approved the new concessions after the airline sweetened the offer. One of Arpey’s first moves as CEO was to call leaders of the flight attendants’ union to his office Thursday to discuss accepting the offer.

It was not clear Friday whether the new leadership and labor deal would be enough to keep American out of bankruptcy for long.

On Wednesday, AMR reported a $1 billion loss for the first quarter — more than half the annual amount of the just-approved labor concessions, which take effect May 1.

Airlines have been hit hard by a downturn in travel caused by the weak economy, the 2001 terrorist attacks, fear of new terrorism around the Iraq war, and the SARS outbreak. Competition from low-fare carriers also has put a lid on prices.

Arpey, who will remain president of American and AMR, said he would work to “restore the confidence of all employees in their great company.”