The Metropolitan Opera’s coming season — and the livelihoods of its workers — continued to hang in the balance on Friday, as the company continued labor talks with two of its biggest unions and a federal mediator in an effort to make progress before a Sunday night deadline.  But the talks with the unions representing the Met’s orchestra and chorus did not go late into the night; they broke up for the day on Friday evening, with plans to resume on Saturday.  Inside the opera house, there was at least a semblance of normalcy, as stagehands returned to work for technical rehearsals of a new production of Mozart’s “Le Nozze di Figaro,” and members of the chorus rehearsed the coming season. Whether they would be back at work on Monday was unclear, though.  Peter Gelb, the Met’s general manager, had postponed the lockout he had threatened for midnight on Thursday, when most of the Met’s union contracts expired, for 72 hours, creating a new deadline of midnight on Sunday. That left alive the possibility that the Met could lock out its workers on Monday, less than two months before the opening of the season on Sept. 22.  Outside the opera house on Friday, the day began with about 150 singers and musicians from the Met’s chorus and orchestra holding a demonstration, with a melodious score, in Dante Park, a small park opposite Lincoln Center.  So far, the Met has come to terms with only three of its unions, those representing ushers, ticket takers, cleaning staff, security guards, building engineers and call center workers. Contracts for 12 unions, including those of the choristers, orchestra players and stagehands, remain unresolved and in some cases seem far from resolution.  Still, there was a palpable sense of relief, however wary, among the choristers and players at the rally on Friday morning. Most wore black T-shirts that read “United — Metropolitan Opera” on the front, with the symbols of the various unions on the back.  A brass nonet from the orchestra played music by Monteverdi, Bizet, Borodin, Verdi and Handel, and union officers, members of the negotiating teams and several elected officials — including Gale A. Brewer, the Manhattan borough president, and Assemblywoman Linda B. Rosenthal — spoke of the Met’s stature and the importance of reaching an agreement.  The only bellicose moment — a chant of “Gelb’s got to go,” led by Ray Hair, president of the American Federation of Musicians, which represents the orchestra — quickly changed course when Mr. Hair said, “But it doesn’t have to be that way” and urged the Met to acknowledge the musicians’ importance to the company’s operation.  The Met said in a statement that it was hopeful that the 72-hour extension of the negotiating period would “allow productive talks with the unions who have not yet reached agreement with the Met.”  Mr. Gelb said in a statement: “We want to work together with union representatives and do everything we can to achieve new contracts, which is why we’ve agreed to an extension.”  James Odom, the president of the American Guild of Musical Artists, which represents the chorus, stage directors, soloists and others, said before the rally, “We’re ready to work out an agreement, but we have to address the real issues.” He was referring to the expansion of the Met’s budget to more than $300 million a year during Mr. Gelb’s tenure. “There are problems that go far deeper than just cutting union wages.”  Jessica Phillips Rieske, a clarinetist in the Met orchestra and a member of the orchestra’s negotiating team, also expressed guarded hope that Allison Beck, the federal mediator who joined the talks on Thursday, would be able to bring the sides together.  “I thought she was very professional, very reasonable,” Ms. Phillips Rieske said. “But we haven’t had negotiations in the mediation process yet, so we’re taking it one day at a time.”  There were indications that Ms. Beck had her work cut out for her. One union, Local 1 of the International Alliance of Theatrical Stage Employees, which had not opted for mediation, partly because both sides had believed its talks were further along, said late on Thursday night that its negotiations had stalled.  And in his first public statement after the lockout was postponed, Tino Gagliardi, the president of Local 802 of the American Federation of Musicians, continued to question the need for significant cost savings at the Met and said it would take more than 72 hours to reach an agreement.  “It is our hope that the mediated negotiations will finally yield transparency on the part of Met management, requiring it to prove why it needs upwards of $30 million in cuts to address a deficit of $2.8 million,” he said.  Mr. Gelb has said that the deficit was kept that low only by record fund-raising in recent years, which cannot be sustained indefinitely, and by dipping into the Met’s endowment, which is no longer large enough to cover the expenses of a single season — a traditional red flag for a performing arts organization. He has said that donors would be willing to double the endowment if they did not fear that the money would be used to plug annual deficits.  In addition, box office revenues are down, and in 2012 the Met took the unusual step of selling $100 million worth of bonds to see it through its financial problems.  An earlier version of this article misidentified the avenue upon which Dante Park is located. The park, across from Lincoln Center, is on Columbus Avenue (at West 63rd Street), not Amsterdam Avenue.  A version of this article appears in print on August 2, 2014, on page A18 of the New York edition with the headline: First Extended Talks at Met End Without a Labor Deal. 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Singers and musicians held a rally on Friday morning, as other Metropolitan Opera workers rehearsed and union leaders prepared for federal mediation.