Verizon workers in nine states could walk off the job as soon as early Sunday if union negotiators don’t reach an agreement over benefits with the wireless carrier.

A contract covering 39,000 Verizon workers represented by two unions expires at the end of Saturday. Last week, the Communications Workers of America announced that 86 percent of Verizon workers covered by the contract voted to strike in a recent poll, if a new agreement isn’t reached.

The contract covers employees in nine states from Massachusetts to Virginia who work for Verizon’s wireline business, which provides fixed-line phone services and FiOS Internet service.

CWA officials announced in a statement Saturday evening that they were waiting for a response from Verizon on a new bargaining proposal they put to negotiators at Rye, New York, on Friday night that the union says would offer the company health care and retiree cost savings.

If there is a strike, Verizon expects its effect on customers to be “minimal,” spokesman Richard Young said Saturday.

“We have done extensive training to prepare for this day, including the training of thousands of nonunion employees,” he said, adding that the company can also reroute calls to call centers not affected by the strike, and resolve some problems remotely.

The unions say the telecom giant is demanding that workers sharply increase their health care contributions and make concession on pensions.

Verizon, the union says, is demanding cuts in jobs and job security and wants to either eliminate the company’s 401k benefit match or freeze its defined benefit pension. In addition, workers might be asked to pay “thousands more dollars” in health care costs due to higher deductibles, co-pays and co-insurance costs, according to the CWA’s website.

But Candice Johnson, a CWA spokeswoman, said preserving jobs is the union’s main priority.

“Workers very much want a fair contract, and this particular negotiation is all about good jobs,” she said. “Verizon is looking to get rid of even more good community-based jobs by extensive contracting out, by offshoring our work.”

Verizon said in a statement Friday it has seen little progress toward a new agreement after seven weeks of negotiations and called the union’s proposals “unrealistic and out-of-touch in today’s marketplace.”

The contract also affects wireline workers in Connecticut, Delaware, Maryland, New Jersey, New York, Pennsylvania, Rhode Island and Washington, D.C.

About 45,000 Verizon workers went on strike in August 2011 for about two weeks.

(AP)