Postal Service and union officials went back to the bargaining table yesterday to launch a tense and difficult search for a contract that could end the threat of a nationwide mail strike.

As the countdown began toward a Sept. 16 deadline for settlement, a special mediator-arbitrator predicted 'tough' negotiations and ruled out any quick progress.

"I think it's safe to say . . . that it's very unlikely that we will be moving to a point of action which will be of particular interest" for several days, said James J. Healy, 62, Harvard professor and veteran labor trouble shooter.

"My present feeling is it is going to be tough" to reach a settlement, Healy said at the conclusion of yesterday's initial session at Federal Mediation and Conciliation Service headquarters.

Healy said he spent the day exploring the disputed issues with the two sides and would do the same at sessions scheduled for today and Monday, Labor Day. He said he did not expect "intensive discussions" to begin until after that.

Leaders of the American Postal Workers Union (APWU), the National Association of Letter Carriers and the Mail Handlers Division of the International aborers Union were looking for a sweeter pay raise than the 19.5 percent like proposed in the rejected three-year pact.

At the same time, officals of the U.S. Postal Service were trying to weaken a no-layoff clause that the unions successfully retained after a bitter fight that led up to the tentative contract accord of July 21.

"I'm not giving a damned thing up on the no-layoff clause," insisted Emmet Andrews, head of the 299,000 member APWU, as he arrived for the opening session.

Shortly before the talks resumed, U.S. District Court Judge John Pratt extended until Sept. 18 his temporary order barring a strike by the two largest unions, the 299,000-member APWU and the 181,000-member letter carriers. Although the order duplicates what already is in the law, it serves as a fresheer, sterner warning ro recalcitrant workers.

Meanwhile, a fourth union that bargained separately with the Postal Service announced that its states leaders have approved the contract rejected by the order unions. The 38,000 member National Rural Letter Carriers Association does not required ratification by rank-and-file members.

Labor and management opened their latest round of talks with Healy under a unique bargaining arrangement fashioned Monday when a strike seemed imminent. The two sides agreed to a 15-day period for either reaching a settlement on their own or letting Healy resolve the dispute for them.

Under the compromise, Healy will try to guide bargainers toward a negotiated settlementve that must be resubmitted for members' approval. But if he decides a settlement cannot be reached within 15 days, he turns into a arbitrator and must draw up a final, binding contract by the 10 a.m. Sept. 16 deadline. In that event, workers would have no ratification vote.

Healy praised the two sides for their apparent sincerity and cooperation in finding a "workable solution" to their dispute.

The rejected contract provided raises and cost-of-living hikes totaling 6.5 percent a year, raising a postal worker's average pay from a current $16,000 a year to $19,200 by 1981.