Three days of contract negotiations between American Airlines and its flight attendants union ended Thursday with no deal.
The airline said it made new offers on pay and health care benefits.
"The company has real money on the table," said spokesman Missy Latham.
Laura Glading, president of the Association of Professional Flight Attendants, said she was angry after the negotiations ended.
"To us, there's a tremendous sense of urgency," she said. "And I feel as though we've been screaming at the top of our lungs from a rooftop for three years, saying, 'We have to get this done.' Flight attendants are suffering. They've been working off a concessionary agreement since 2003. But is there a sense of urgency on the part of the company? There has not been. We are not going to quit."
The talks, held at a Nashville hotel, were the first in seven months.
American’s 18,000 flight attendants have been negotiating a new contract for two years.
Last year, they voted overwhelmingly to authorize a strike.
Leaders of the Association of Professional Flight Attendants asked federal mediators to declare an impasse and release them from negotiations, a necessary step before a strike could occur.
No decision was made on the union’s request.
In the last negotiating session in May in Washington, American offered flight attendants a 3 percent bonus to sign the contract and a 9.9 percent pay raise over five years. But differences remained over work productivity, health care and other benefits.
The next step is up to the mediator, who was expected to schedule another round of talks in the coming months.