U.S. District Court Judge Terry R. Means said Wednesday that American was likely to win a lawsuit seeking to stop the election among passenger-service agents, so he granted a temporary restraining order.
American says the union didn't get enough signatures to qualify for an election under new, tougher rules that took effect in February.
The National Mediation Board had scheduled voting to begin June 21 and run through Aug. 2.
The Communications Workers of America are seeking to represent nearly 10,000 agents who take reservations and work at airports. It's the largest group of nonunion workers among American's 73,000 employees.