A federal judge, declaring yesterday that a labor settlement at The Washington Star was in the "public interest," set a deadline of 4 p.m. today for The Star's management to complete negotiations with its employes' 11 unions.

At the end of an extraordinary day of legal proceedings and last-ditch bargaining, Judge Charles R. Richey warned that unless The Star and the unions met his deadline, he would consider issuing a temporary restraining order to prohibit The Star from carrying out its threat to shut down on New Year's Day or take other legal action.

Richey interrupted the hearing in his federal courtroom at midafternoon to summon representatives of several unions and the newspaper's management to a courthouse lounge in an attempt to overcome remaining bargaining obstacles. "You better get in there right away. I will give you an admonition. The court expects you to resolve this dispute. You hear me?" Richey said as he ordered the unusual negotiating session.

Although top officials of The Star, four unions and the Federal Mediation and Conciliation Service hurriedly gathered in the courthouse lounge, they failed to settle the outstanding, they failed to settle the outstanding disputes. Richey then announced his deadline of 4 p.m. today.

Turning to Star publisher George W. Hoyt, who at the time was seated in the witness stand in Richey's federal courtroom, the U.S. District Court judge said, "I hope you won't disappoint your associates and superiors and, most importantly, the court in reaching a resolution of this by 4 o'clock."

Time Inc., the publishing firm that bought The Star earlier this year, has announced it will close the newspaper Monday unless all 11 unions representing 1,270 full-time Star employes approve severely modified new labor contract by noon Sunday. Neither contract by noon Sunday. Neigher Hoyt nor any other Star official made a statement yesterday suggesting any relaxation of The Star's deadline.

Several major unions that represent Star employes, including the Washington-Baltimore Newspaper Build and Teamsters Local 69, have already approved new five-year contracts. The guild, which represents about 475 news, advertsing and other white-collar workers, ratified tis contract yesterday by an overwhelming 262-to-10 margin.

Shortly after Richey announced his 4 p.m. deadline, Wayne L. Horvitz, director of the Federal Mediation and Conciliation Service, called for leaders of all 11 Star employe unions to meet this morning, warning that a bargaining deadlock would endanger The Star's "survival" and the livelihood of hundreds of Star employes.

The mediation service had already begun preparations for such a meeting before Richey announced his deadline. In fact, the midafternoon gathering at the U.S. Courthouse yesterday interrupted Star negotiations with the Teamsters, mailers and operating engineer's unions that were already under way at FMCS headquarters, leaving some union negotiators bewildered.

Despite the gravity of the labor disputes, yesterday's proceedings had comic moments. Richey joked with witnesses, asking one Star Official whether he considered his job "permanent" or "temporary" in view of The Star's threat to close. At one point, he threw his court open to questions about his actions. "You ever hear of a judge giving you a press conference in open court?" he asked later.

The court proceedings stemmed from a bitter dispute between The Star and one of its major unions -- Columbia Typorgraphical Union No. 101, which represent about 175 Star printers. The union has asked Richey for an injunction barring The Star from closing.

In a legal memorandum yesterday, the typographical union charged that The Star "is using the threat of a shutdown as an economic weapon to compel the union to surrender contract rights." Moreover, in a letter made public during the court proceedings, union President William J. Boarman indicated he viewed management's shut down threat as a bluff. "We have not and do not believe that you intend to close The Star," Boarman said in the letter.

The Star responded in a court nemorandum, asserting that the CTU "has displayed the most substantial intransigence of any of the Star's union." The company accused the CTU of instituting its lawsuit "rather than seeking progress at the bargaining table."

Central to the bargaining disagreement, according to union officials, is a Star proposal to eliminate 80 printing emplyes by June and cut its printing staff to as few as 25 jobs during the next five years.

The union has objected, saying that its members were previously guaranteed lifetime jobs at The Star under an existing contract and that The Star's new demands mean many printers will be "forced" to give up the lifetime jobs they were promised. Management has proposed to offer $40,000 "buyouts" to any Star printer who quits.

In seeking an injunction to stop The Star from shutting down Jan. 1, the union has argued that such a move would violate several provisions of its existing contract and that the issue of whether The Star may close down and discharge its employes is subject to arbitration.

In a legal memorandum, The Star contended that if the newspaper does close and if an arbitrator later finds the shutdown to have been illegal, "the arbitrator would have remedial power sufficient to cure the violation and could force the Star to reopen and make all employers [financially] whole." The Star conceded that such an arbitration ruling would be a "drastic remedy."

Star officials agreed in court yesterday to submit the issue to arbitration, but said such arbitration proceedings may not occur until after The Star's Sunday deadline for its threatened closing.

Part of yesterday's court testimony by Star officials provided new estimates of The Star's current and future financial losses. Star officials have previously cited the newspaper's heavy deficits in demanding new contracts from the unions.Star controller Wayne Gray testified yesterday that The Star lost $7.2 million in the first, 11 months of 1978 and said it expects to run a $16 million deficit next year.

This amount would significantly exceed the loss The Star reportedly incurred in 1974, when it was taken over by Texas businessman Joe L. Allbritton. Allbritton sold The Star to Time Inc. this year for about $28 million.

Despite the continuing labor disputes between The Star and several key employes' unions, the newspaper has already made considerable progress in concluding new contracts. The newspaper has 14 existing contracts with its employes' 11 unions.

It is seeking to replace all 14 contracts with new, modified agreements by Sunday. According to union, Star and other officials, the newspaper has already reached preliminary, tentative or final agreement on at least eight new contracts with seven unions.

In addition to the contracts with the Teamsters and the Newspaper Guild, new agreements have reportedly been approved by unions representing maintenance workers, electricians, garage mechanics, equipment machinists and "firemen" who operate heating equipment. A preliminary accord has been reported with the photoengravers' union.

In addition to the talks with the printers' union, negotations between The Star and the pressmen's union have been reported to have encountered the stiffest obstacles.