Nine years after Verizon promised to make its high-speed Fios internet service available to every household in New York City, the city sued the company on Monday, saying it had failed to keep that pledge.

In a complaint filed in New York State Supreme Court in Manhattan, the city contends that Verizon is in breach of a 2008 franchise agreement. That contract called for Verizon to build a citywide Fios network by the end of 2014. But, the city says, Verizon has failed to make its service available to at least “tens of thousands” of prospective customers and has refused to accept service requests from many others.

For two years, city officials have been pressing the company to satisfy its obligations, in the hope of avoiding litigation. But the two sides reached an impasse this winter, and on Monday the contentious tone of the standoff became public.

“Verizon must face the consequences for breaking the trust of 8.5 million New Yorkers,” Mayor Bill de Blasio said in a statement. He added that, “It’s 2017 and we’re done waiting. No corporation — no matter how large or powerful — can break a promise to New Yorkers and get away with it.”

Verizon responded sharply. A company spokesman, Raymond McConville, said in an email that “on a day where the city is preparing for the biggest blizzard of the season, it’s sad that the mayor’s focus is on pursuing a frivolous lawsuit.” Verizon also hinted that it might choose not to renew its city franchise in three years.

Verizon said the de Blasio administration was interpreting the contract differently from the way the previous administration, that of Michael R. Bloomberg, had. “The de Blasio administration is disingenuously attempting to rewrite the terms of an agreement made with its predecessor and is acting in its own political self-interests that are completely at odds with what’s best for New Yorkers,” the company said in a statement. “We plan to vigorously fight the city’s allegations.”

Verizon does not dispute that large numbers of New York residents have been frustrated by their inability to receive the company’s heavily promoted Fios internet and television services. But the company lays much of the blame on landlords who have not granted Verizon access to run cable across their property.

Verizon says it has already met its obligation to run fiber-optic cable past every home in the city. It argues that the contract did not call for it to connect that cable to every house and apartment building in the city.

In a letter sent last week to Anne M. Roest, the commissioner of the city’s Department of Information Technology and Telecommunications, the company said it had spent “more than $3.7 billion to install thousands of miles of fiber-optic cable” and other equipment across the city. “As a result, we now pass all households in the city and can provide service to over 2.2 million households within seven to 14 days of receiving a service request,” said the letter, signed by Craig L. Silliman, Verizon’s general counsel.

Verizon also noted that it employed 4,000 people in the city and said that it planned to spend an additional $1 billion over four years. But, Mr. Silliman wrote, “the city’s intransigence does not create a favorable environment” for negotiations of a franchise renewal, which could begin as soon as next summer.

Some city residents have been complaining for years about their inability to persuade Verizon to provide high-speed internet service to their homes, said Susan Lerner, executive director of Common Cause New York, a good-government advocacy group. “People continue to be very frustrated because it appears that Verizon is motivated by what will be most profitable for them — what buildings to wire and what buildings to ignore,” Ms. Lerner said.

She said that city officials had clearly tried to avoid taking Verizon to court, but that they had given up trying to persuade the company to complete the network.

“This really is about undertaking an ambitious obligation and then deciding halfway through that it’s not worth it,” Ms. Lerner said. “We are very happy to see the city holding the vendor’s feet to the fire. This is absolutely what should be done.”