Mr. Cuomo is not the first politician or the first governor to take that position, but newly passed state legislation will make it easier for him to do so.
The meeting was the first high-level meeting between Entergy, the company that runs Indian Point, and the Cuomo administration, and it was convened at Entergy's request.
Mr. Cuomo has repeatedly taken the position in speeches that he wants to close the plant. But his administration had not delivered the message so directly to the company, or in such strong words, and company officials left the meeting alarmed.
The encounter seemed to mark a heightened determination to close the plant, and recent events put considerable leverage in the governor's hands to make his wish a reality.
On the day of the meeting, lawmakers were in the process of approving legislation to streamline the siting of new power plants in New York, a step that, for the first time in nearly a decade, makes replacing Indian Point and the huge amount of power it generates more feasible. The last siting law expired at the beginning of 2003.
At the same time, the licenses for Indian Point's two reactors expire in 2013 and 2015. The state can derail the process by refusing to provide permits related to the plants' use of water from the Hudson River as a coolant. Last year, the State Department of Environmental Conservation rejected a crucial permit application from Entergy; the company is challenging the move.
For the Cuomo administration, closing Indian Point would be a major step toward reshaping the state's energy policy. Replacing the plant would take years and require a long-term energy strategy. The plant produces 2,000 megawatts and provides 25 percent of the power in New York City and Westchester.
Public worries about the plant, in Buchanan, about 35 miles north of Midtown, flared after the recent catastrophe at the Japanese nuclear plant in Fukushima, and after a report highlighting the Indian Point plant's proximity to a fault line. But replacing it with natural gas plants or other more conventional options could bring its own environmental and emissions concerns.
Josh Vlasto, a spokesman for Mr. Cuomo, said "the governor's long-standing position with respect to closing Indian Point has been clear, and this administration intends to follow through with implementing that policy."
Details of the meeting last week between Entergy and the governor's advisers were provided by people who were briefed on it but who insisted on anonymity because the meeting was private. It took place at the Capitol office of Howard Glaser, the governor's director of state operations. The top Entergy executive at the meeting was Richard Smith, the president of its wholesale commodity business.
James F. Steets, a spokesman for Entergy, issued a general statement defending the plant.
"Indian Point provides 25 percent of N.Y.C.'s and Westchester's power for subways, schools, police stations and firehouses, businesses and homes with virtually no emissions, at lower cost," he said. "Entergy's investment in recent years of more than a half-billion dollars to upgrade safety and security, and rigorous independent inspections by multiple inspectors on site full time, help ensure Indian Point is safe."
The Atomic Energy Act of 1954 gives the federal government sole authority to regulate the safety of nuclear plants, but the states have always had the right to approve or disapprove the construction of power reactors, as they can approve or disapprove any power plant. Several states have held referendums on whether to force nuclear plants to close, but no such proposal has ever passed. Vermont is declining to permit continued operation of the Vermont Yankee plant, owned, like Indian Point, by Entergy, for operation beyond the expiration of its license next spring.
Entergy needs a water quality permit from New York as part of the federal relicensing of Indian Point. Last year, the administration of Gov. David A. Paterson denied the permit, but Entergy has requested an administrative hearing, which will take place this year. The company is also contesting the state's denial to the Nuclear Regulatory Commission. The Cuomo administration will preside over the endgame of this process at a critical phase, as Entergy seeks relicensing for Indian Point.
The passage of power plant legislation last week gave the Cuomo administration important new ammunition in its battle. While no large plants have been sited in New York State in more than a decade, the new legislation, by streamlining approvals, makes it easier for energy companies to begin that process.
But David Lochbaum, the director of the nuclear safety project at the Union of Concerned Scientists, an advocacy group, said the challenge of replacing Indian Point had more to do with transmission of existing power than generating power. Local resistance has prevented the building of new transmission lines to bring power from the north to New York City and its suburbs.
"If you took Indian Point out of the mix, one of the options would be to replace it with more power from upstate New York or Canada, but the power lines are already at capacity," Mr. Lochbaum said. "The power might be there, but not the ability to get it to people who need it."
The Cuomo administration is supporting a plan to connect New York City and New Jersey with transmission lines beneath the Hudson, which could deliver 660 megawatts to Manhattan. That plan, also, is controversial.
The Indian Point plant uses up to 2.5 billion gallons of water from the Hudson per day as a coolant, cycling it back into the river. Richard L. Brodsky, a Westchester Democrat and former assemblyman, has sued the N.R.C. over its issuance of exemptions to Indian Point from health and safety requirements. Mr. Cuomo filed a brief supporting the suit when he was attorney general.
Matthew L. Wald contributed reporting.