Using the power of the bully pulpit, Gov. Mark Dayton and Minneapolis Mayor R.T. Rybak urged musicians and management of the Minnesota Orchestra to settle on a contract.

“Get in a room and talk to each other,” Rybak said at a Thursday news conference, echoing comments he made last week. “There is no excuse not to sit at a table and get this solved now.”

Dayton revealed that he had met with each side separately last week and delivered the same message — that they must meet with mediator George Mitchell, the former Senate majority leader. Dayton said he has been in phone contact with Mitchell frequently in the last few days, but did not know whether negotiating sessions had been scheduled for this week.

“We’re not going to take sides,” Dayton said. “There are legitimate interests and concerns on both sides, but this has to be about more than self-interests.”

According to musicians ­spokesman Blois Olson, “Both sides are talking through the mediator.” Speaking after the news conference, Olson did not offer specifics. “The mediator’s process is confidential.”

Dayton and Rybak have grown increasingly frustrated by the labor dispute, one of the longest in state history.

“The future of the Minnesota Orchestra is at stake,” Rybak said.

Musicians have been locked out for nearly a year in a contract dispute and the entire 2012-13 artistic season was canceled. Orchestra management estimates that musicians have lost $12.4 million in salary and benefits since being locked out last Oct. 1. The organization itself lost an estimated $6 million in concert revenue, according to the Minneapolis convention and visitors bureau. A report by the agency estimated the Minneapolis Convention Center, where concerts were to have been held last year, lost just under $900,000 in anticipated revenue from October 2012 to July 2013. Losses to dining establishments were estimated at $1.7 million and for parking revenue, $414,000.

Orchestra management issued a statement thanking Dayton and Rybak for their encouragement.

“We agree that it is only through immediate and intense negotiations that we will reach settlement, and the board negotiating committee is ready to meet,” the statement said.

Last weekend, the orchestra’s board made a third proposal to musicians, through Mitchell’s office. Details were not offered, and the union is still studying the offer. Musicians have rejected two previous ­proposals.

Asked why he and Rybak are speaking out now, Dayton said: “This has gone on too long.”

Music director Osmo Vänskä has said he would resign if the orchestra was not back rehearsing by Sept. 30. Management had indicated early this month that a deal would need to be struck by Sept. 15 in order for that to happen. That deadline passed on Sunday.

Olson made a vague reference to “new board members” stepping up over the weekend to try to resolve the crisis. On Thursday, he said he did not know details and management has not commented on the matter.

Rybak said at Thursday’s news conference that a “game of brinksmanship is being played and we are dancing very close to the cliff.”