Mr. Johnson, who is exploring a run for mayor in 2021, said that in his district, which includes the High Line, there are “apartments that are crumbling and apartments 50 feet away that are selling for millions of dollars.”

Mr. Hoylman’s legislation would create a sliding tax surcharge: For properties valued between $5 million and $6 million, a 0.5 percent surcharge would be added on the value over $5 million. Fees and a higher surcharge would apply to homes that sold for more than $6 million, topping out at a $370,000 fee and a 4 percent surcharge for homes valued at more than $25 million.

The office of the city comptroller, Scott M. Stringer, estimated that a pied-à-terre tax would bring in a minimum of $650 million annually if enacted today. “For us, $650 million a year is a lot of money to deal with things such as our subway crisis,” Mr. Stringer said, “but it’s a rounding error for the people who own these expensive part-time apartments.”

The people most likely to be affected by the tax are the “international elite” who can afford it, he said.

There were 75,000 pieds-à-terre in New York City in 2017, up from 55,000 such units in 2014, according to the New York City Housing and Vacancy Survey. In spite of the increase, the share of pieds-à-terre that comprise vacant units unavailable for sale or rent remained at about 30 percent in both years.

Mark Levine, a city councilman who represents Upper Manhattan, will propose in a forthcoming white paper that money from a pied-à-terre tax should be dedicated to fixing the city’s public housing stock and to create affordable housing. “Even the Victorian-era robber barons who built all these mansions were living there,” Mr. Levine said.

And because the city’s property tax system is antiquated, co-ops and condos are not taxed at their true market value, but on the income generated by similar rental buildings. A property tax reform commission is currently studying how to revise the city’s tax system.

“I would argue they need to pay more than the baseline property taxes because the value of the real estate depends on the viability of New York City, the quality of the public services, and they are not effectively carrying their weight for that,” said James Parrott, director of economic and fiscal policies at the Center for New York City Affairs at the New School, and a member of the property tax reform commission.

New York City is the second largest location of Mr. Griffin’s firm, Citadel. The company has been expanding in the city, recently acquiring more space at an under-construction Midtown office tower on Park Avenue; company officials suggested that commercial real estate taxes, combined with the taxes that Mr. Griffin will pay on his apartment, amounted to a significant contribution to New York City. Zia Ahmed, a spokesman for Mr. Griffin, declined to comment.

Mr. Parrott, who wrote a 2014 paper for the Fiscal Policy Institute that was the basis of Mr. Hoylman’s legislation, estimated that Mr. Griffin would have to pay $8.9 million per year if there was a pied-à-terre tax.

New York State does have a so-called mansion tax, a 1 percent tax levied on homes that sell for $1 million or more. That tax brought in $1.1 billion for New York City from the 2016 fiscal year to present, according to the Department of Finance.

Mayor Bill de Blasio, a Democrat who says income inequality will be the most important issue leading to the 2020 presidential election, has called for an expansion of the mansion tax, using Mr. Griffin’s apartment purchase as an example of what is “fundamentally broken in our country.”