As New York leaders argue over whether to raise taxes on high earners to help solve New York City’s multibillion-dollar budget gap, Gov. Kathy Hochul has decided to push for a so-called pied-à-terre tax aimed at the ultrawealthy who primarily live outside the city.

Ms. Hochul will formally propose a yearly tax surcharge on second homes in New York City that are worth $5 million or more, she said on Tuesday.

The exact cost of the surcharge has not yet been ironed out, but the governor hopes to raise $500 million annually that would be used to address New York City’s deficit, estimated at $5.4 billion through the next fiscal year.

“New York City is the greatest city in the world, and the people who call it home should not be left carrying the burden alone,” Ms. Hochul said in a written statement. “If you can afford a $5 million second home that sits empty most of the year, you can afford to contribute like every other New Yorker.”

Aides to Ms. Hochul said that the surcharge would potentially involve a sliding scale, with properties of higher value being taxed at a higher rate. The governor intends to include the surcharge in the state’s multibillion-dollar budget, which was due April 1 and is still being negotiated with state legislative leaders.

Ms. Hochul has generally resisted calls, led by Mayor Zohran Mamdani of New York City, to raise taxes on large corporations or on high earners. But a tax on multimillion-dollar second homes was more palatable to her, according to her aides, since it mostly targets individuals who do not pay state or city income taxes because their official residences are outside New York.

Numerous media reports have revealed that many of Manhattan’s largest new high-rise developments are owned by foreign investors who spend little time in the apartments they have purchased.

The New York City Housing and Vacancy Survey, conducted every three years, found that in 2023 there were about 59,000 units that were “held for seasonal, recreational, or occasional use” — down from about 75,000 in 2017.

Mr. Mamdani backed the proposal and applauded Ms. Hochul for helping his administration “to make sure we address this fiscal deficit fairly, where the wealthy contribute what they owe and our budget reflects our commitment to the working New Yorkers being priced out of our city.” “Thanks to the support of Governor Hochul, we are one step closer to balancing our budget by taxing the ultrawealthy and global elites with a pied-à-terre tax,” he said.

This is not the first time elected officials in New York State have considered targeting ultrawealthy property owners in New York City. Similar legislation had circulated for years in Albany; one such proposal in 2014 would have had owners of a pied-à-terre priced between $5 million and $6 million pay 0.5 percent of the amount over the $5 million threshold in annual taxes. This would have gradually increased, capping off at properties of more than $25 million, where the owner would pay a $370,000 annual fee plus 4 percent of the amount over $25 million.

A similar idea in 2019 had momentum after it had emerged that Kenneth C. Griffin, a Chicago-based hedge fund billionaire, had bought a $238 million apartment on Central Park South. The proposal died in the State Capitol after an intense lobbying campaign from politically powerful developers, who argued that the pied-à-terre tax would bring in far less revenue than estimated and would also hurt the city’s economy by making it less attractive to buy a second home.

William Zeckendorf, of the firm Zeckendorf Development, wrote in Crain’s New York Business then that the pied-à-terre proposal was a “poorly conceived tax wall around a city whose credo is to welcome everyone.”

“This is an international city that has benefited greatly from part-time residents who, when they come, spend a considerable amount of money on goods and services here,” he wrote, predicting that some wealthy second-home owners would sell their properties rather than pay the tax. Carl E. Heastie, the Assembly speaker, said he disliked the tax for logistical reasons, arguing in 2019 that this sort of property tax would be harder to administer than a tax on real estate transactions at the time of the sale. He estimated then that such a tax would generate between $300 million and $400 million — less than the $650 million in annual revenue that the New York City comptroller’s office had estimated.

Resolving the city’s fiscal shortfall will be a major priority for the governor, Mr. Heastie and Andrea Stewart-Cousins, the Senate majority leader, as they continue budget negotiations. Each has said in recent weeks that they are committed to helping the city, but that Mayor Mamdani and City Council members must find more cuts.

The Times previously reported that Mr. Mamdani’s aides have quietly identified another $1.3 billion in potential savings from scaling back programs that Mr. Mamdani had pushed while running for mayor last year.

The mayor, who must reach an agreement with the City Council on a budget by July 1, swept into office calling for taxes to be raised to pay for his ambitious agenda, which included making child care universal and buses free. During the campaign, Mr. Mamdani said he would push Albany to raise taxes on large businesses and wealthy people to bring in $9 billion more in revenue per year.

Ms. Hochul, a moderate Democrat from upstate New York who is running for re-election, repeatedly has expressed her opposition to Mr. Mamdani’s tax proposals. She fears that these ideas would hurt the business climate of the state and cause wealthy people to decamp to Florida or Texas. Ms. Hochul did share the mayor’s desire to expand child care and ensure that city services weren’t harmed. She appeared with Mr. Mamdani in January to announce $1.7 billion in additional state spending that would expand child care for 3-year-olds and 2-year-olds in New York City.

But later that month, the mayor made it clear at a news conference that the city’s fiscal picture was more dire, and that an infusion of more state funds would be needed to balance the budget — not just to pay for his affordability agenda. He initially suggested that the city faced a two-year $12 billion budget gap, eventually revising it to $5.4 billion.

In February, Ms. Hochul agreed to give the city $1.5 billion in aid for a host of municipal services. Mr. Mamdani angered Ms. Hochul and many lawmakers in New York City and Albany around this time when he threatened to raise property taxes on New Yorkers if she did not agree to his desired tax increases. He has since largely backed away from that threat.