WASHINGTON — 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 Communication 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.

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

Verizon said in a statement Friday it is “preparing for all scenarios” ahead of the contract’s expiration. The company said 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 affects wireline workers in Pennsylvania, Connecticut, Delaware, Maryland, New Jersey, New York, Rhode Island, as well as Washington, D.C.

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