NEW YORK (CNN/Money) - American Airlines pulled back on its bankruptcy deadline Tuesday, allowing the flight attendants' union a second chance to ratify a contract calling for $340 million in concessions that the airline says it needs to avoid a bankruptcy filing.

The world's largest airline and the union, the Association of Professional Flight Attendants, said that the new electronic vote would be concluded by late Wednesday afternoon. The airline had said it was prepared to file for bankruptcy if all three of its unions hadn't agreed to new cost-cutting contracts by midday Tuesday, but extended the deadline to allow the new vote.

American, based in Fort Worth, Texas, also made millions of dollars in scheduled debt payments due Tuesday.

"With almost 10,000 jobs hanging in the balance, and the future of 100,000 employees at stake, we agreed to take this risk and make this investment for our employees because we believe that all employees will be better off if we can save jobs and restructure our costs consensually rather than through the bankruptcy process," said a statement from Don Carty, chairman of American parent AMR Corp. "This is our last chance to avoid bankruptcy."

But Carty said that with additional debt payments due Wednesday, "I must make completely clear that if we fail to secure flight attendant ratification by tomorrow, we are -- regrettably -- left with no alternative but to immediately file for bankruptcy."

The two other major unions at American -- the Allied Pilots Association and the Transport Workers Union, which represents most American ground workers, approved the concession deals, but the rank and file for the APFA voted narrowly against the proposal. Management and the leadership of all three unions agreed to the new vote by the APFA in meetings that stretched throughout Tuesday afternoon.

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The other two unions had allowed members to change their vote throughout the voting process, as American agreed to new terms to make the six-year contracts more attractive if it is able to recover its profitability. But APFA had not been able to let members change votes and needed the new vote in order to get allow members to vote on the new terms of the deals.

Even if the world's largest airline is forced to file for bankruptcy court protection, the move would have only limited immediate impact on its customers. American intends to file under Chapter 11 bankruptcy, allowing it to continue operations. But, longer term, a bankruptcy filing could force the Dallas-based carrier to make deeper cuts in flight schedules and routes in an attempt to satisfy creditors and lenders.

A filing, if it occurs, would likely wipe out American's investors. Most bankruptcy filings leave little for holders of the company's equity, although some companies in Chapter 11 bankruptcy are able to have their shares continue trading for weeks or even months after filing.

Trading in the stock of American parent company AMR Corp. (AMR: Research, Estimates) was halted on the New York Stock Exchange. The shares, which jumped 40 percent earlier in the day, were up 33 cents, or 10.7 percent, at $3.41 when trading was halted late Tuesday afternoon before details of the flight attendants' vote was released.

The union deals were designed to save American $1.8 billion annual through a combination of across-the-board pay cuts and changes in work rules, which would the airline to cut additional employees.

The leadership of the three unions had only reluctantly endorsed the deals, reached on March 31, arguing to their members that work conditions would be even worse if the airline followed through on its threat to file for bankruptcy. The airline says it will need an additional $500 million in annual labor cost savings if it does file for bankruptcy in order to satisfy lenders who would fund their operations throughout court-supervised reorganization.

"There is no question that these agreements represent a major step backwards for our union," said a statement from James Little, director of the Air Transport Division for the TWU. "We made these agreements only because it is painfully obvious that the results of bankruptcy proceedings would have been far worse. The company has been provided with everything it needs to survive. We can only hope that they will not squander the opportunity our members have provided them."

The 26,000 flight attendants are being asked to approve $340 million in labor cost savings under the concession contracts. The 13,000 pilots voted 69 percent in favor of a contract that is expected to save American $660 million in annual labor costs. The 35,000 members of the TWU, including mechanics, baggage handlers and other ground employees, narrowly approved a deal that will save American $620 million annually.

The Association of Professional Flight Attendants vote was very close, with rejection of the contract getting 9,842 votes, or 51 percent of valid votes cast.

If it does file, American would be the third major carrier to seek bankruptcy protection in the last year, following No. 2 United Airlines, a unit of UAL Corp., which filed in December, and No. 7 US Airways Group, which filed for protection in August but emerged from bankruptcy court protections last month. Air Canada filed for protection from creditors earlier this month as well.

Even with the new labor agreements, American admits it faces a difficult financial road ahead, and that it might still be forced to seek bankruptcy court protections if it can't negotiate new agreements with lenders and suppliers.

Tuesday the company's outside auditor, Ernst & Young, said in a Securities and Exchange Commission filing that the company's current financial condition is tenuous enough to, "raise substantial doubt about the company's ability to continue as a going concern."

The major airlines that operate a large network of hubs severing extensive locations to accommodate business travelers have been having trouble supporting the costs of those systems for more than two years as demand for business travel -- and the fares those travelers were willing to pay -- fell. Increased competition from lower-cost, low-fare carriers, such as Southwest Airlines and JetBlue Airways, is causing significant problem for the so-called "network" carriers such as American.

Neither AMR nor most of the other major network carriers have reported a profitable quarter since 2000, nine months before the Sept. 11 terrorist attacks caused a sharp drop in demand for travel and further financial problems. Last month's U.S. attack on Iraq also caused further erosion in demand for air travel, particularly on international routes.