A strike at American, the nation's No. 2 airline, is one of several looming labor disputes that put four major U.S. carriers at risk of service disruptions this spring.
The Association of Professional Flight Attendants' (APFA) said 96 percent of nearly 18,000 ballots received from its 23,000 members, the highest turnout in union history, were in favor of allowing union leaders to call for a strike.
American Airlines said it looked forward to resuming mediated negotiations next week.
No strike is imminent because of federal airline labor laws that require both sides to remain in talks until the National Mediation Board determines there is a stalemate and releases them from mediation. A 30-day "cooling off" period follows before the union can strike.
The APFA has asked to be released from mediation, but the National Mediation Board has scheduled renewed talks for March 2-3 in Chicago, and for March 12-14 in Washington D.C.
"The gap that remains is significant The issues that remain are pay issues, retirement issues, and scheduling issues," APFA President John Ward said at a press conference to announce the strike vote. He denied reports that most pay issues had been settled.
American and the APFA have not negotiated since December.
American Airlines has said it is ready to return to negotiations and awaits a counter-offer to its latest contract proposal, made in November. At that time the union criticized the offer as a repeat of a tentative agreement rejected by members in September 1999.
On Thursday, American said it was pleased to be returning to the talks, and said reaching a settlement was a "top priority." It added that it was prepared to meet continuously throughout the next rounds.
The four airlines combined carry more than two-thirds of the 588 million domestic passengers who travel on U.S. airlines annually.
The unions believe it's highly unlikely they could all go on strike at once, but it did happen once during the 1960s.
The prospect of major disruptions led the White House to begin conferring with the National Mediation Board, The Washington Post has reported. A series of strikes would spell trouble for a slowing economy.
President Bush said earlier this month he would "explore all options" to prevent a stoppage if the unions and airlines are unable to settle their differences.
The first pending strike could come as early as next month if an agreement is noreached between Northwest Airlines and the Aircraft Mechanics Fraternal Association, which represents about 9,500 mechanics and cleaners.
United Airlines and its mechanics went back to court Thursday. The mechanics, whose contract came up for renewal last July, have appealed to the mediation board to declare an impasse in the negotiations giving them the right to strike.
At Delta Air Lines, the 9,500 pilots represented by the Air Line Pilots Association International also are seeking to be released from mediated talks to strike if a contract agreement is not reached.