The purchase program, which still requires approval from federal officials, would be among the most ambitious ever undertaken, not only in scale but also in how Mr. Cuomo would be using the money to begin reshaping coastal land use. Residents living in flood plains with homes that were significantly damaged would be offered the pre-storm value of their houses to relocate; those in even more vulnerable areas would be offered a bonus to sell; and in a small number of highly flood-prone areas, the state would double the bonus if an entire block of homeowners agreed to leave.

The land would never be built on again. Some properties could be turned into dunes, wetlands or other natural buffers that would help protect coastal communities from ferocious storms; other parcels could be combined and turned into public parkland.’

In the aftermath of Hurricane Sandy, which swept through the region on Oct. 29, Mr. Cuomo has adamantly maintained that New York needs to reconsider the way it develops its coast. He has repeatedly spoken, in blunt terms, about the consequences of climate change, noting that he has responded to more extreme weather in his first two years as governor than his father, Mario M. Cuomo, did in his 12 years in the job. Last month, in his State of the State address, he raised the prospect of home buyouts, declaring “there are some parcels that Mother Nature owns.”

“She may only visit once every few years,” Mr. Cuomo said, “but she owns the parcel and when she comes to visit, she visits.”

Mr. Cuomo’s proposal comes as lawmakers, disaster experts and residents debate what steps New York should take to fortify itself against extreme weather. The Cuomo administration has enlisted experts to study a range of approaches, from installing storm barriers with movable gates to returning oyster beds to some of the state’s shoreline.

Any reshaping of the coastline will be not only costly, but also difficult. Many residents of shoreline communities in New York City and on Long Island live in homes that have been passed along from generation to generation, and are not eager to hear government officials suggest that they move elsewhere, even voluntarily.

“There is a loyalty here,” said Harvey Weisenberg, a longtime lifeguard in Long Beach, N.Y., who represents the storm-tossed community in the State Assembly, as a Democrat. “There’s an expression: we have the sand in our shoes. Once you’re here, you never want to leave, and if you do leave, you want to come back.”

Aides to Mr. Cuomo met with federal officials in Washington on Friday to present their hurricane response plan, including the proposed buyout program, which would be paid for using a portion of the $51 billion disaster relief package approved by Congress last week.

The Federal Emergency Management Agency has financed the purchase of homes in disaster-stricken areas for two decades. Hundreds of property owners in upstate New York decided to pursue buyouts after Tropical Storms Irene and Lee, though no sales have been finalized, according to state emergency management officials.

But Mr. Cuomo is proposing a far broader program for homeowners affected by Hurricane Sandy, using money from the federal Department of Housing and Urban Development, an agency Mr. Cuomo once headed. The governor’s office plans to market the program, holding information sessions in local neighborhoods to inform residents of the buyout option.

The use of federal housing money for a buyout program requires approval from the Department of Housing and Urban Development. The governor’s office said federal officials seemed receptive to their proposal, and that Mr. Cuomo hoped the program would be approved and that he could announce details in the next two weeks.

A spokesman for the Hurricane Sandy Rebuilding Task Force, which President Obama created in December, said Sunday that it is too soon to say whether the state will be allowed to proceed.

“It’s premature to speculate on whether this particular plan would be approved,” the spokesman, Brendan C. Gilfillan, said by e-mail. Mr. Gilfillan said that the federal housing agency needed some time because “prior to Friday, New York state had been slower to share its plans” than New York City and New Jersey; the Cuomo administration said it is in regular communication with federal officials about its plans, and believes it is moving more quickly than other jurisdictions.

For the 10,000 or so homes in the 100-year flood plain that were substantially damaged by Hurricane Sandy, Mr. Cuomo would offer owners the pre-storm full market value of their houses. Homeowners who chose to relocate within their home county would receive a 5 percent bonus above the market value, as part of a government effort to encourage them to stay nearby. State officials said they were planning for the possibility that 10 to 15 percent of those eligible would take the buyout.Residents of more vulnerable areas would receive a further enticement: they would be allowed to sell their homes even if the homes suffered little, or possibly even no, damage from the hurricane, and the state would pay them an additional 10 percent bonus, above market value, to sweeten the deal.

In a few dozen blocks located in areas of extreme risk, the state would offer another 10 percent bonus if every homeowner on the block agreed to sell. Local officials would be expected to determine how best to use the new open space, though they would not be allowed to build on it.

“They could say, ‘Let’s put a park on that block,’ ” said a high-ranking state official, who spoke on the condition of anonymity because Mr. Cuomo had not yet announced the program. “Suddenly it’s a community asset instead of a potential source of damage and pain.”

Lawmakers from storm-ravaged neighborhoods said they welcomed the program, though, in most cases, they expected a relatively small number of residents to participate. They said buyouts could appeal to residents worried about rising flood insurance premiums, as well as those who have listed their homes for sale in recent months, only to find potential buyers willing to pay only a fraction of what they might have offered before the storm. (The program is not targeted at the most expensive waterfront homes; it would cap the payments for houses at around the median home value in a given neighborhood.)

On the eastern shore of Staten Island, virtually an entire neighborhood, the Fox Beach section of Oakwood Beach, has decided it wants to move. In the neighborhood, which has long been tormented by routine flooding as well as brush fires, 133 of 165 households have signed up to take a buyout if one is offered, according to Joseph Tirone Jr., the leader of the Oakwood Beach Buyout Committee.

Another committee member, Tina Downer, said, simply, “We don’t have the fight enough to stay any more.” Ms. Downer said her house, set about 300 yards from the shoreline, was inundated by a storm surge of at least 13 feet, and said she has now concluded that the neighborhood  should “return to nature and do what it was intended to do, which is to be a sponge.”

But in the Rockaways, Cynthia Koulouris, a resident for 41 years, said she was not going anywhere, even though her basement flooded and her neighbor’s house burned down during the storm.

“Nobody wants to leave here,” she said. “Where would I go? To Astoria? To Brooklyn? No!”

Kirk Semple and Vivian Yee contributed reporting from New York.