The Broadway stagehands union voted unanimously yesterday to authorize its union leadership to call a strike if necessary, and with “thunderous applause” vowed to stop work as of December if there is no contract agreed to with a group that represents the theater owners, a spokesman for the union said.

The strike authorization vote gives Local One’s international office the power to formally call for the strike. The spokesman, Bruce Cohen, said the international office’s president is a “strong supporter” of Local One. The local leadership also could call a work stoppage, but Mr. Cohen would not say when that might occur.

Last week, the theater group, the League of American Theaters and Producers, announced it would begin imposing portions of its final contract offer today. Yesterday, the league released a summary of its offer, which includes stipulations governing electrician duties, overtime hiring requirements, and pay schedules and duties for rehearsals and work calls. On Friday, the union posted a letter backstage in theaters claiming it was “under attack” by the league. In response, Executive Director Charlotte St. Martin said in an interview the league is implementing the work rules to ensure the shows on Broadway continue despite the ongoing impasse.

Both parties have indicated they are open to further negotiations, but no dates have been set.

In a statement, Ms. St. Martin said that the league does not want the theaters to go dark. “All shows will continue to perform until and unless Local One walks out,” she said. “The responsibility for a decision to shut down Broadway rests squarely with Local One.”

The possible work stoppage would affect only the theaters owned by the Jujamcyn and Shubert companies, which account for 22 of the 39 Broadway theaters. On Thursday, the Nederlander Organization, which runs nine theaters, announced it would not impose the work rules. The group has a separate contract with the union, but was sitting at the negotiating table as an observer. Should the theaters go dark, the union also voted to authorize spending $1 million, in addition to authorizing use of its $4.15 million defense fund for its own members, to pay benefits to union workers on Broadway.

The stagehands could also find work elsewhere in the city on television and in productions, including at Radio City Music Hall and Lincoln Center, Mr. Cohen said. The parties have been at odds since they submitted what they said were final contract offers on October 9. They have been arguing over whether stagehands should be paid for the work they physically do, as the league says, or whether a theater can hire stagehands daily regardless of whether work is available.

Mayor Bloomberg has offered for the city to mediate the negotiations, as he did in 2003 when the musicians’ union went on strike for five days. The league is interested in pursuing the offer, Ms. St. Martin said, but the union has “respectfully declined” the offer, Mr. Cohen said.