An endangered Carnegie Hall appearance is applying fresh pressure to the Minnesota Orchestra’s lingering labor dispute.

Music director Osmo Vänskä has said the orchestra must be in rehearsal by Sept. 30 to be ready for the early November concerts. To make that happen, orchestra management said Wednesday that it would need to reach agreement with its union musicians by Sept. 15.

The concerts became entangled with Vänskä’s fate when he said in an April 30 letter that he would resign if Carnegie canceled the concerts because of the labor lockout. Vänskä has said nothing about his plans since that letter, and management did not indicate Wednesday whether Vänskä remains committed to resigning if the concerts are imperiled.

“Osmo is the only person who can answer that question,” CEO and President Michael Henson said.

Vänskä, music director since 2003, is widely cited as a key factor in the orchestra’s growing international reputation.

The musicians have been locked out since contract negotiations broke down last Sept. 30.

Also on Wednesday, the union released a statement focusing on a mid-August proposal by former U.S. Sen. George Mitchell, who was brought in to get the parties back to the negotiating table. Mitchell is best known for brokering a peace agreement in Northern Ireland.

“The musicians accepted the independent proposal from management’s selected mediator, while management rejected it,” the statement said. “Under the mediator’s proposal, all of the key deadlines for the fall season would be met, ensuring the Carnegie residency and Osmo’s tenure.”

That proposal would have lifted the lockout and returned musicians to work for two months beginning Sept. 1, under salary terms of the old contract. If no deal was reached in that time, musicians would have worked for another two months with a 6 percent pay cut. If there still was no deal on Dec. 31, presumably the lockout would resume.

Henson would not comment on whether Mitchell’s proposal was discussed at Wednesday’s board meeting. “The process with Senator Mitchell remains confidential,” he said.

Parallel tracks

The timeline announced Wednesday arose from conversations among Henson, Vänskä and representatives of Carnegie Hall.

“This was mutually agreed upon, but the main decisionmaker is the music director,” Henson said.

Referring to the parallel-but-related nature of the Carnegie dates and the contract talks, Henson said the deadline was established to give artistic leadership time to prepare.

“The second step is the contract negotiation,” he said.

Musicians have said they will not bargain under a lockout. Management has said it will not lift the lockout. Mitchell is seeking a compromise to create a window during which the two sides could negotiate. Since management rejected his first proposal, he has held confidential discussions with each side.

Negotiations on a contract started on April 12, 2012. Citing structural deficits, management proposed cutting base salaries by 32 percent. Musicians have not made a counterproposal, although they would agree to do so if they returned to the table under the terms suggested by Mitchell.

Vänskä’s work with the orchestra has received critical and public acclaim, locally, nationally and internationally. He is considered the foremost interpreter of his Finnish countryman, composer Jean Sibelius. The orchestra’s recordings of Beethoven and Sibelius have been nominated for Grammys. A previous trip to Carnegie won plaudits for the orchestra’s sophistication. Over the course of four concerts at Carnegie — two in November and two next April — the orchestra was to perform all seven of Sibelius’ symphonies, which they also are recording for the BIS label. September recording sessions with BIS were canceled last week because of the lockout.

Also hanging in the balance of the labor dispute is the opening of the newly renovated Orchestra Hall. The Symphony Ball, a major gala fundraiser, is scheduled for Sept. 20 at the hall.