Labor negotiators for 14 San Francisco hotels offered Thursday to keep employee contributions for health care at $10 a month but left open the possibility that workers would be responsible if costs increased beyond 10 or 12 percent a year.

Union officials said the refusal to guarantee a cap was unacceptable, ensuring that the prolonged dispute would drag on.

Mike Casey, president of Unite Here Local 2, representing 4,300 members who have returned to work for a 60-day cooling-off period after a strike and lockout at the 14 hotels, acknowledged that the employers' proposal represented "some movement on their part, but it is not enough to get us close to an agreement.''

The two sides do not meet again until Jan. 6, and the cooling-off period expires Jan. 23. Until then, the union has agreed not to strike and the hotels have promised not to impose another lockout.

Matt Adams, managing director of the Hyatt Regency Hotel and vice president of the hotels' bargaining unit, said the hotels had proposed a four-year contract that would "completely eliminate any increase in employee contributions" for health coverage.

The workers' contribution has remained at $10 a month for 20 years, and the union has been dogged about keeping it there. The hotels have proposed shifting more costs to workers throughout the negotiations.

But the hotels' latest offer has a complication. The hotels said they would cover increases in health care costs up to 10 percent in the first year and 12 percent in the second, third and fourth years of a contract. Any increase above that would bring a cut in benefits or force workers to make monthly co-payments, Casey said.

The union was more receptive to a hotel proposal to lower the monthly total an employee must work to qualify for health care to 45 hours from the current 80 hours.

"We want a contract in this cooling-off period, and the union must step up and show good faith and bring this to a resolution,'' Adams said. "The idea of dragging this on is unacceptable. The proposal is a very good deal, and the union should take notice and think of its members' needs.''

When the two sides began negotiations, employers were proposing that workers' contribution be $32 a month in the first year and $273 a month by the end of the contract.

Management's four-year contract offer is a shift away from its insistence on a five-year deal. The union, along with Unite Here locals in Los Angeles and Washington, D.C., wants a two-year contract that would put it in a negotiating cycle with hotel unions in six other major cities and Hawaii and thus strengthen its hand.