“The members of I.A.T.S.E. want to save the Met, that’s why we will be at the bargaining table in coming days hammering out an agreement that works for all,” he said in a statement. “A lockout would be a serious setback, an opera tragedy likely resulting in a lost season and a long-term loss of operagoers for years to come in Lincoln Center and on theater screens around the globe.”

The Met, which has struggled at the box office in recent seasons and drawn heavily from its endowment, which is no longer sufficient to cover a year’s expenses, wants to cut labor costs. It says it needs to reduce expenses, so it can convince the donors it is increasingly reliant on to build up its endowment. The unions are resisting the proposed cuts, and several have questioned Mr. Gelb’s management, noting that ticket sales have declined despite new initiatives that helped increase the company’s budget to more than $300 million a year.

While opening night is not until Sept. 22, when a new production of Mozart’s “Nozze di Figaro” is scheduled, a work stoppage would disrupt the company’s preseason rehearsal schedule. The chorus is already back at work rehearsing, and technical stage rehearsals of a new production of a double bill of “Cavalleria Rusticana” and “Pagliacci” are set to begin next week.

A work stoppage would be the first at the Met since 1980, when a labor dispute with the orchestra led to a bitter 11-week lockout that delayed the opening of the opera season until December. The Met previously had a strike in 1969.

A lockout would have perils for both sides. It took years for the Met to recover the subscribers it lost during the 1969 strike. More recently, an angry 16-month lockout damaged the Minnesota Orchestra. But a lockout at the Met would also leave its union workers without paychecks and benefits at a tough time.

The Met’s letter contained an attached memo from the its human resources department saying that in the event of a work stoppage, unionized workers covered by the Met would lose their health insurance unless they decide to pay for insurance under the federal Cobra law, which would cost $1,255.33 a month for individuals and $2,793.10 a month for families. It said that depending on how people are paid, their last paycheck would come either on July 31 or Aug. 7.