The flight attendants' vote was announced after unions representing pilots and ground workers said Tuesday that they had approved even deeper cost-cutting deals.
The flight attendants' union said the concessions deal was rejected by fewer than 500 votes out of more than 19,000 cast.
But the union had complained Monday that some members were having trouble casting votes by phone and the Internet. It asked American to extend voting then, but American denied the request.
By Tuesday afternoon, however, the situation appeared to have changed. James C. Little, the top official for the union representing American's ground workers, said the flight attendants would be allowed to keep voting until 5 p.m. Wednesday.
American officials had vowed to file for bankruptcy as early as Tuesday if any of its three major unions rejected concessions designed to cut American's labor costs by $1.8 billion a year, or more than 20 percent.
Company officials did not respond to calls for comment.
In late afternoon, the New York Stock Exchange halted trading in the stock of American's parent, AMR Corp.
Directors of the flight attendants' union's convened an emergency conference call that was still going after 2 and 1/2 hours, a spokesman said.
Another source close to the situation who spoke on condition of anonymity said flight attendants were considering ways to reconsider the tentative agreement without triggering a bankruptcy filing.
Workers voted over the past two weeks whether to ratify tentative agreements that called for layoffs, steep wage cuts and reduced benefits.
Leaders of American's three main unions had reluctantly supported the concessions as a better alternative than bankruptcy. They feared that American could use the bankruptcy process to impose even harsher cuts and reduced pension benefits.
The Allied Pilots Association said its members approved the concessions 69 percent to 31 percent. The union said 10,200 pilots, a high turnout, took part.
The margin was narrower - 53 percent to 47 percent - among ground workers, the Transport Workers Union said on its Web site Tuesday morning.
"To willingly take our airline and our company into bankruptcy would not be a better alternative," John Darrah, president of the pilots' union, said while announcing the results of the pilots' voting. "There is no upside to bankruptcy."
But angry employees packed union meetings to complain that terms of the concession deals were too harsh. They objected to the length of the deals -- nearly six years -- and small raises in later years.
American sweetened the deals last week by offering one-time bonuses of up to 4.5 percent in 2006 or later if the company's credit ratings improve sharply.
American was seeking $660 million in concessions from its 12,000 pilots, $620 million from 34,000 ground workers and $340 million from 24,000 flight attendants. The agreements include layoffs for 2,500 pilots, about 2,000 flight attendants and up to 1,400 ground workers.
American chairman and chief executive Donald J. Carty had warned that if American went into bankruptcy, it would seek $500 million in additional labor concessions. Darrah said he feared bankruptcy would mean another 500 to 1,500 pilots would be laid off.
American has been battered by a weak economy, terrorism and competition from low-cost airlines on 80 percent of its routes. Those factors have hit hard at business travel, which was a lucrative part of American's business.
American says it has cut other costs $2 billion per year. It was negotiating with suppliers and aircraft lease holders for more favorable terms, and even offering stock options to suppliers.
However, American's Fort Worth-based parent AMR continues to lose about $5 million a day and has lost nearly $5.3 billion in the past two years.
Labor concessions were expected to avert an immediate bankruptcy filing but would not improve American's weak revenue and might not solve its long-term problems, analysts said.
In a report disclosed Tuesday, auditors for AMR questioned the company's ability to stay in business, citing large losses and the need to cut labor costs.
Auditor Ernst & Young LLP also raised doubt about whether AMR could meet a $1 billion liquidity requirement for an $834 million line of credit.
The auditors' comments were included in AMR's annual report filed with the Securities and Exchange Commission.