The dancers and management of American Ballet Theatre last night agreed on a new labor contract, averting the specter of a disbanding of the half-century-old troupe that had been raised by board action late last week.

The new contract, for three years ending Oct. 31, 1993, calls for 36 guaranteed weeks of employment each year (with supplemental benefits for the rest of the year) for the troupe's 83 dancers; a 10.5 percent wage increase over the life of the contract, staggered during the final year to bring the wage scale to 13 percent above current levels; increases in overtime, daily meal allowance and other ancillary benefits; and a two-year waiver of some provisions affecting hotel accommodations and travel allowances on two specific projected foreign tours.

The major concession on the part of the dancers appeared to be this last point, yielding on past insistence on single rooms for each dancer, but only on foreign touring and limited to two years.

In contrast to some of the inflammatory statements on both sides reported during recent stages of the negotiation, the two parties seemed to welcome the new agreement in a wholly amicable spirit.

Speaking from ABT's New York offices, where the agreement was concluded last night, dancers committee representative Victor Barbee said:

"I think all of us, all the dancers, are very relieved and delighted. The vote was 65 dancers for, 4 against. I think these were very successful negotiations for all sides. The dancers were able to maintain the integrity of provisions won in past negotiations, but at the same time we were able to offer much-needed financial relief for the company, without interrupting the performance schedule. We understand the precariousness of the company's financial situation, and were quite willing to help out. Given the economic climate today, we think we've reached a very good agreement under the circumstances."

ABT Director Jane Hermann said: "I'm very glad we're all settled. It's a fair settlement, and we're going back to work tomorrow. Of course, we've still got a lot to do to bring the company back to a wholesome fiscal operation. But the important thing is that over the last 12 months we have avoided adding to the deficit; in fact, the board was able to bring in an additional $1 million in contributions to offset potential backsliding. Our only deficit now is an accumulated one of the past, more than $4 million. We realize we are going to have to have a much more organized, more concentrated kind of fund-raising in coming years, and that's what we're planning on now. But the company is already being operated so that the burgeoning spending has been stopped -- I can say with impunity that the company is under control.

"This will mean operating very tightly over the next couple of years. We won't be able to afford risky programming; we'll do very good programming, but it will be within responsible limits -- it must. We are encouraged that subscription sales this year are already up across the board."

Hermann said the operating budget for the 1990-91 season would be under $17 million.

Company rehearsals are scheduled to begin today for a national tour that starts with the coming Kennedy Center Opera House engagement Jan. 15-27, a highlight of which will be a new full-length production of "Coppelia" staged by Enrique Martinez, with sets by Tony Straiges and costumes by Patricia Zipprodt.