DALLAS (AP) — The pilots’ union at Southwest Airlines is asking federal mediators to open the way for a strike, saying that big differences remain over pay and other items despite three years of bargaining over a new contract.

The request Thursday by the Southwest Airlines Pilots Association doesn’t mean a strike is imminent, even though union members voted nearly unanimously in May to authorize a strike.

If mediators grant the union’s request, pilots could strike but only after a 30-day cooling-off period, during which the White House could delay a walkout or Congress could impose a settlement on both sides.

Southwest opposed the union’s request.

Adam Carlisle, Southwest’s vice president of labor relations, said the two sides are meeting regularly and the company has proposed industry-leading compensation and changes in pilot scheduling. He said further mediation will drive negotiators closer to an agreement that helps both sides.

The union’s move is the strongest step yet toward a strike by any of the major pilot unions, which are seeking large pay raises as travel and airline revenue rebound from the pandemic.

Earlier this year, pilots at Delta Air Lines ratified a contract giving them raises of 34% over four years. United Airlines pilots are still bargaining, and the union for American Airlines pilots is considering whether to hold a ratification vote on a tentative agreement between the airline and union negotiators.

In a letter to mediators, union officials said Dallas-based Southwest has been “evasive” and refuses to seriously discuss pay, work rules and other topics.

Dallas-based Southwest has more than 9,300 pilots.