Federal mediators have set the stage for a new showdown between Eastern Air Lines and its pilots union in an apparent effort to try to force a settlement in a labor dispute that has threatened the airline's efforts to survive.

The National Mediation Board, heading off a bankruptcy court action on Eastern's labor contracts yesterday, began a process that would free the pilots to strike and Eastern to unilaterally change the terms of its contract with the pilots at the end of a 30-day cooling-off period unless a new contract can be reached by then.

Eastern had planned yesterday to ask U.S. Bankruptcy Court in New York to abrogate the contract with the Air Line Pilots Association but withdrew that action after the mediation board's declaration of an impasse late Sunday.

The declaration, in effect, makes it possible for Eastern to walk away from collective bargaining with the union without going through a court hearing. Under the federal law governing collective bargaining in the airline industry, the declaration of an impasse starts a 30-day clock ticking. If no new agreement is reached at the end of that period, the union is free to strike and the company is free to impose its final offer.

The Eastern pilots union's leadership group voted yesterday to send out a strike ballot after negotiations broke down again earlier in the day. The majority of the union's members spent most of 1989 on picket lines honoring a strike by the International Association of Machinists. The IAM struck Eastern on March 4, 1989, virtually shutting down the carrier and forcing it to file for protection from its creditors under federal bankruptcy laws.

The bankruptcy court installed a trustee, Martin Shugrue, to run the failing airline in April, after the creditors told the courts they had lost confidence in the airline's management under Frank Lorenzo.

Shugrue has maintained since then that one of his primary goals was to seek labor peace at the airline, where it has been absent for some time.

But efforts to resolve differences with the pilots have been unsuccessful. In the meantime, another group is seeking to replace ALPA as the bargaining unit for the pilots.

Jack Suchocki, chairman of the pilots bargaining committee, said yesterday that Shugrue's statements about labor peace were apparently "just a stalling tactic, because what we're seeing is simply a continuation of the Lorenzo approach to labor relations." He said that the pilots were ready to continue talks with the company during the 30-day cooling-off period.

Eastern, which continues to lose more than $1 million a day, is scheduled to present a business plan to its creditors Friday.