A theater owners group said last night it would begin imposing portions of its contract offer to a stagehands union, adding to worries of a shutdown on Broadway should the union respond with a strike.

The executive director of the League of American Theaters and Producers, Charlotte St. Martin, called the move “the next logical and responsible step.”

“It is our strong preference to have a contract with Local One, and the implemented portions of the final offer at least give us some of the flexibility we need,” Ms. St. Martin said in a statement. “We are forced to implement because Local One will not pursue meaningful change.”

Both parties have been at odds since they submitted what they said were final contract offers on October 9. Both have said they are open to further discussions, and would prefer to avoid a strike by the union or a lockout by the producers.

The union will vote Sunday on whether to authorize a strike.

The president of the union, James Claffey, Jr., found out about the league’s decision in a phone call from Mayor Bloomberg, who again offered for the city to mediate the dispute. Mr. Claffey declined the offer.

“We negotiate our own contracts, and we’re perfectly willing to sit down with the League anytime they are willing to negotiate,” a spokesman for the union, Bruce Cohen, said.