Representatives of Radio City Entertainment and its orchestra’s union met with a mediator for the first time yesterday after Mayor Bloomberg made an effort to help resolve an impasse between the two sides.

Having acknowledged that they were not close to an agreement, management and union officials reported to Gracie Mansion early yesterday. The mayor said he had asked a former city schools chancellor and president of St. Francis College, Frank Macchiarola, to act as the mediator.

“I went with all of them into the room and just said, ‘Look, the city cannot get involved in private labor negotiations, but it’s in the city’s interest to have companies succeed and people working, and to have the great events that bring tourists to the city continue,” Mr. Bloomberg said.

Negotiations went into the night with no sign of a resolution, and a spokesman for the union, Local 802 of the American Federation of Musicians, said no deadline had been set for an agreement.

Mr. Bloomberg’s move was a repeat of his actions during the labor dispute between the musicians’ union and Broadway producers in 2003, when he set them up for a bargaining session in Gracie Mansion with Mr. Macchiarola acting as mediator.

The 35 members of the Radio City orchestra have been out of work for nearly two weeks after they walked out of a dress rehearsal for the “Christmas Spectacular,” the 10-week holiday show featuring the famed Radio City Rockettes. They attempted to return for the opening performance the next day, but management locked them out, citing the possibility of a future work stoppage. The show has used canned music ever since.

Although management has said it considers the musicians to be on strike, union members said they agreed to a proposal and are ready to sign a contract. The proposed agreement included a higher salary, continued overtime pay, and year-round health benefits.

Radio City Entertainment would not comment on discussions with the union, saying only that negotiations are ongoing. The mayor said he had offered to get involved earlier, but that the two sides told him they wanted to negotiate privately. They agreed that if they had not settled the dispute by last Friday, the mayor would provide a mediator and a venue for discussions.

“I will not get further involved, nor should I,” Mr. Bloomberg told reporters yesterday in Queens. “I think it’s up to the two parties in a private dispute. The city can facilitate, and that’s what we’re trying to do.”