Verizon workers in nine states have voted to go on strike if necessary over a dispute about a new contract, a union official said at a rally Saturday.

“Our members are clear and they are determined,” said Dennis Trainor, an official with the Communications Workers of America union. “They reject management’s harsh concessionary demands.”

At the rally in New York, the CWA announced that 86 percent of Verizon workers who voted in a recent poll backed strike action if required. A contract that covers 39,000 workers represented by the CWA and the International Brotherhood of Electrical Workers expires at midnight on 1 August.

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 that the internet company is demanding that workers sharply increase their health care contributions and make concessions on pensions.

Verizon spokesman Rich Young said that the company had made the unions “a solid proposal that recognizes the changing communications landscape and offers a path toward success.”

Many of the aspects of the contracts that were set “decades ago” were no longer relevant in an industry that was facing increased pressure and structural change, Young said. He also said that the company had been training non-union employees to take on additional roles to ensure that there was no disruption to customers in the event of a strike.

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

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