"It is clear that achieving cost competitiveness will require additional job reductions over time," she said. "The details of how we achieve the required savings and the potential impact on United's workforce, however, are still under discussion, and it is premature to comment on specifics."
In a recorded message to employees this week, Peter D. McDonald, United's chief financial officer, said that despite the cuts the airline has already made, "it may be more difficult as we go forward," he said.

United Airlines has been in bankruptcy protection for nearly two years. The carrier is planning to cut more jobs and is examining the possibility of eliminating four of its employee pension plans.
(M. Spencer Green -- AP)
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Four of United's employee pension plans also may be targeted for elimination. Last month the airline said it was considering eliminating the four plans, a move that would wipe out about $2 billion in future retirement benefits for many of its 120,000 retirees and workers.
Leaders of the union representing United's flight attendants this week said they had lost confidence in management and wanted the senior executives removed.
US Airways, based in Arlington, is trying to extract about $800 million in annual cost savings from its employees by the end of the month. The airline said that if it fails to get those cuts, which are part of its $1.5 billion restructuring plan, it will have to file for bankruptcy.
After nearly a week of round-the-clock negotiations at the Key Bridge Marriott in Rosslyn, US Airways executives and leaders of its pilots union continued to negotiate on concessions yesterday. The pilots' leaders plan to meet today to discuss whether to send the airline's final proposal to the rank and file for a vote. The carrier is seeking $295 million a year in concessions from its pilots.
Also pressuring the airline is a $110 million pension payment due Sept. 15. Later this month, the carrier must be able to show it has reduced its costs enough to meet requirements of a $900 million loan guarantee granted by the Air Transportation Stabilization Board.
Earlier this week, US Airways executives dismissed a proposal from its machinist union suggesting operational changes that the group said could save the airline $115 million. Robert Roach Jr., general vice president of the International Association of Machinists and Aerospace Workers, which represents US Airways' mechanics, said slashing employee pay and benefits is a bandage that doesn't fix the airline's long-term operational problems.
"You can't expect employees to make sacrifices when they see those sacrifices being wasted," Roach said. "You can't restructure this industry on the backs of its employees."
US Airways spokesman David Castelveter said that there was nothing "new, unique or innovative" about the mechanics' proposal and that the mechanics' suggestions would have added expenses rather than reduced them. The airline said the only way to reduce its costs is through cuts in pay and benefits across its labor groups.
Delta Air Lines continues to negotiate with its pilots in the hope of securing $1 billion in annual pay and benefit cuts from the union. As early as next week, chief executive Gerald Grinstein is expected to unveil a new strategic plan, which some close to the carrier said may include the elimination of jobs and a reduction in flights as well as a possible bankruptcy filing. Yesterday, Delta executives renewed their request with bondholders to change their lending agreements, part of the airline's effort to restructure about $20 billion in debt.
As the airlines struggle to find their way, the ripples will spread. "The one who is going to take this the worst, besides the bankers and the Wall Street investors, is the airline employees," said Darryl Jenkins, visiting professor at Embry-Riddle Aeronautical University in Daytona Beach, Fla. "They're the ones who are going to be the walking wounded for a long time to come."