The main union at Verizon, the Communications Workers of America, issued a statement soon after the 12:01 a.m. deadline, saying that it would “stop the clock” and that negotiations would resume later on Sunday.

The contract covers workers from Maine to Virginia who are represented by the Communications Workers and the International Brotherhood of Electrical Workers.

At 12:21 a.m. Sunday, the Communications Workers reported progress on major issues, including protecting health care coverage for active and retired workers and strengthening job security provisions in the contract.

That union, which represents 50,000 of Verizon’s 65,000 unionized workers, was holding talks in Rye, N.Y., and Washington.

In a statement issued several minutes later, Verizon said, “We continue to negotiate in good faith to achieve new contracts for our employees.”

While both sides expressed optimism about reaching a settlement without a strike, the Communications Workers said in a statement, “Significant additional bargaining still lies ahead before a settlement is possible, particularly in the areas of employment security and union jobs and recognition.”

Shortly before 9 p.m. on Sunday, Eric Rabe, a Verizon spokesman, said, “There are very serious negotiations going on, and we remain optimistic.”

Verizon has insisted that its unionized workers contribute toward health insurance premiums and that its retirees shoulder more of the cost of their health insurance.

Another issue was that Verizon had moved thousands of union jobs to nonunion contractors or to the company’s Verizon Business division, which is largely nonunion. The Communications Workers complained that this trend was undercutting its bargaining clout.

The unionized employees work for the most part in Verizon’s traditional landline side of the business, while its fast-growing Verizon Wireless division has few unionized employees. For years the union has pushed Verizon to agree to ways to make it easier to unionize employees at Verizon Wireless.

The unions have threatened a strike as Verizon gears up to provide television service in the five boroughs of New York City to compete with other cable providers. Verizon, which has nearly 230,000 employees nationwide, recently obtained a 12-year franchise from state regulators in which it promised to make its television service available to all of the city’s 3.1 million households by 2014.