Musicians of the Minnesota Orchestra on Tuesday said they had given management a counterproposal on a new contract.

Management disagreed, calling the communication a “vague framework for a proposal that calls for wage increases over three years.”

“We confirmed the minimum level of restoration for musician compensation after they have been without salary or health care” since the lockout began nearly a year ago, musicians’ spokesman Blois Olson said in an interview.

Citing a confidentiality pact agreed to by both sides, Olson would reveal no other details, but he said the union considered the offer to be a “financially specific” proposal. That is significant because the musicians had never offered a counteroffer in their standoff with management.

“Our legal advisors say that the Union has offered nothing that would constitute an official counterproposal,” Michael Henson, president of the orchestra, said in a statement. “They have suggested vague terms around one element of the contract (seeking salary increases) but have not responded in any way with regard to proposed work rule alterations, insurance premiums, individual contracts, additional pay practices or benefits.”

Henson said a request for a pay increase at this stage is “extraordinary.” The board’s latest proposal would cut annual minimum salaries by 25 percent. Musicians voted that down last week.

Regardless, both sides agree there was an exchange of information that seems to indicate the two sides are communicating. Neither side would say whether it means they are negotiating directly with each other or through former U.S. Sen. George Mitchell, who has offered to mediate.

Orchestra management has said it needs an agreement by Sunday in order to get musicians back on stage by Sept. 30. That is the date by which music director Osmo Vänskä has said he would need musicians rehearsing so they would be ready for November concerts at Carnegie Hall. If those concerts are canceled, Vänskä has said he will resign.

Minneapolis Mayor R.T. Rybak, in an earlier interview about Vänskä’s fate, said that the two sides need to negotiate.

“Both sides have to stop looking for others to bail them out,” Rybak said. “There have been many people who have stepped in over time, but all have reached the conclusion that this will only be solved by the two sides at a bargaining table. Lock yourself in a room and shut up about it until you come back with a solution. The community is disgusted and desperate.”

The mayor, who helped to organize a concert celebrating the orchestra’s Grammy nomination last February, said, “We have to have dramatic change from both sides. We are in a serious crisis.” He said the public nature of the dispute has been corrosive.

“I’m a former reporter, but the constant communication through the media has built such hostility that this cannot be solved by someone from the outside,” he said.