SAN JOSE — The union that represents the majority of Santa Clara County’s approximately 15,000 full-time public employees has voted overwhelmingly to authorize a strike to protest the county’s latest labor contract involving pay and benefits.

Officials with the county chapter of SEIU Local 521 said the two-day vote, completed Tuesday night, was 96 percent in favor of a strike. They would not say how many of the union’s 9,000 members, most of which are full-time workers, submitted ballots. But a posting on the union’s website by one chapter chair indicated almost 3,200 members had voted overall.

The contract with the union, which has repeatedly been extended since it expired in June, ended Tuesday, and the union does not want to extend it. Both the union and the county confirmed the next bargaining session is scheduled for Friday.

Clariessa Mariscal, an employment counselor for the county and a chief union steward, said while the vote authorizes the union’s bargaining team to call a strike, union rules require a second vote by its members before any action could occur.

Union officials could not say when or if that might happen.

“The strike is the last thing anyone wants,” Mariscal said. “We are passionate about what we do and the community we serve. We are willing to do what it takes and we don’t want to strike.”

Mariscal said the union is seeking a contract “that will recruit and retain a talented workforce.” The union opposes the proposed increases in healthcare and retirement costs, though Mariscal declined to say what those increases were.

“At the end of the day, we want a package that includes fair wages and retirement security,” she said. “All working families would relate to that.”

But Deputy County Executive Luke Leung said that under the now-expired contract, members of the eight groups of workers represented by SEIU — including public health nurses, 911 operators and child support officers — either have no cost or minimal cost for health-care premiums.

County officials are seeking an increase in those payments, to employee pension payments, to the county’s $1.8 billion retiree health care debt, and to extend the vesting time that would allow employees to retire with free medical care for life, among other goals.

SEIU Local 521 union officials said they have been negotiating with the county since late April. Luisa Blue, the union’s chief elected officer, was out of town and unavailable for comment.

Leung said none of the SEIU workers are prohibited by law from striking. But, he said, if the union decides to strike, the county can petition the state’s Public Employment Relations Board to seek a court injunction to prevent certain essential health and safety workers from striking because their absence would impact the public.

Leung said he is hopeful that an agreement can be reached “under terms that we both can live with.” He said the last time this union authorized a strike vote was two years ago, but no strike occurred.

Union officials said the last time Santa Clara County workers represented by SEIU went on strike was in 1975, and the strike lasted more than two weeks.

The threat of a strike comes on the heels of a three-day strike by Hayward city employees that began Tuesday to protest that city’s labor contract, also involving health care and retirement benefits the city is seeking from its workers. That strike, which is expected to end Thursday, follows a strike by two unions that shut down BART for 4 1/2 days at the start of July. On Sunday, a judge ordered BART workers to say on the job for the next 60 days, averting another strike.

On Tuesday, the county Board of Supervisors approved a contract with the 1,500-member County Employees Management Association and a non-union group of 125 employees who work as confidential administrative staff.

Contact Tracy Seipel at 408 275-0140.