For his annual State of the State speech in 2018, Mr. Cuomo’s office was exploring how it might introduce different forms of so-called congestion pricing, including fees on for-hire vehicles, according to a Cuomo administration official who was not authorized to discuss the matter publicly. A decade ago, Mayor Michael R. Bloomberg pressed for an $8 congestion fee for drivers in parts of Manhattan during peak hours, but the measure was defeated in Albany.

Mr. Gianaris said state lawmakers should not wait until the next session to take up the mayor’s proposal.

“I would argue that the M.T.A. is in a full-blown crisis and that would justify our return to Albany to enact this measure in an emergency session,” Mr. Gianaris said.

Scott Reif, a spokesman for Senate Republicans, said the city should not discuss raising taxes when it had a large surplus.

“If the city wants to up its contribution to help shore up the subways for commuters and their families — which we support — it certainly has the means to do that,” Mr. Reif said in a statement.

The proposed new tax would raise about $700 million to $800 million a year, with more than $500 million going toward capital costs for subways and buses and about $250 million for the half-price MetroCard program, city officials said. It would increase the city’s highest income tax rate by about half a percentage point, to 4.4 percent from about 3.9 percent, for married couples with incomes above $1 million and individuals who make more than $500,000.

City officials estimate that the tax would be paid by about 32,000 New York City tax filers, or fewer than 1 percent of those who file their taxes in the city. New Yorkers already contribute to the authority through various taxes and fees, and the city has committed $2.5 billion for the agency’s current capital improvement plan.