Unionized employees at Washington area Safeway and Giant Food stores voted Wednesday to authorize a strike against the grocery chains if the two parties fail to agree on a new contract.

The United Food & Commercial Workers International Union has been locked in contract negotiations with Giant and Safeway for several weeks. The biggest point of contention, officials familiar with the negotiations said, has been the rising cost of health-care benefits. The officials were not authorized to speak publicly about the talks.

The vote “does not mean that a strike will occur, but it lets Safeway know loudly and clearly that members are ready to take this step if they determine it is the only way to get a decent contract,” UFCW Local 400 said in a statement.

On Tuesday, the two sides announced that the contract, which expired Oct. 31, had been extended through Dec. 20. UFCW Local 400 represents 17,000 area Giant and Safeway employees.

“Giant has a long history of working together with unions to reach collective bargaining agreements that are fair and reasonable for all parties,” said Jamie Miller, a spokesman for Land­over-based Giant. “We are encouraged by the progress we are making with the UFCW local unions at the bargaining table.”

The negotiations have been “productive,” Greg Ten Eyck, a Safeway spokesman, said in a statement.

“The bargaining teams are dealing with very complex issues, and Safeway is committed to attempting to address the concerns of the unions,” Ten Eyck said. But the company must also “mitigate the cost advantage of non-union retailers, who in recent years have entered the region and taken market share from traditional grocers like Safeway.”

Meanwhile, both Safeway and Giant have hired temporary workers to fill in if there is a strike.

“While we don’t want a work stoppage, and don’t think there’s a reason for one, we must be prepared to keep our stores open in that event,” Ten Eyck said.