Mr. Cuomo didn’t specify which taxes the state would look to increase, and his aides didn’t answer subsequent questions. Layoffs and borrowing will also be part of the discussion, he said.

State lawmakers adopted a $178 billion budget in April that depended upon additional federal aid that hasn’t materialized. The spending plan gave the Cuomo administration unilateral authority to withhold state payments to contractors, schools, municipalities and social-service providers if the U.S. Congress didn’t act.

Mr. Cuomo and Democratic leaders of both the state Assembly and Senate have repeatedly said they wouldn’t adjust their budget until there was another relief bill. Negotiations in Washington have proceeded in fits and starts; a bipartisan group of lawmakers is working on a $908 billion bill that would dedicate $160 billion in funding for state and local governments. On Tuesday, Treasury Secretary Steven Mnuchin presented a new $916 billion White House proposal to House Speaker Nancy Pelosi (D., Calif.) which included the same amount of state and local funding.

New York state’s budget office estimated in October that the coronavirus is responsible for a $13.5 billion drop in state revenue from its February projections. New York is projecting an $8.7 billion deficit for the fiscal year that begins on April 1. That figure could almost double, because it assumes the state will find $8 billion in recurring savings in its current fiscal year, according to David Friedfel, director of state studies for the Citizens Budget Commission, a fiscal watchdog group.

Mr. Cuomo said during a press conference Wednesday that he was counting on Congress to fill at least some of the current year’s hole, but acknowledged that additional actions will need to occur.

“If Washington gives us some of it, then we’re going to have to redo a budget, we’re going to have to raise taxes—I believe we’re going to have to raise taxes, at the end of the day, in any event,” Mr. Cuomo said. “The question is, how much in tax?”

The governor must propose a budget in January for the upcoming fiscal year.

Almost half of the state’s revenue comes from its personal income tax, which is projected to bring in around $60 billion before refunds in both the current and upcoming fiscal years, budget documents show. Assembly Speaker Carl Heastie, a Democrat from the Bronx, and Senate Majority Leader Andrea Stewart-Cousins, a Democrat from Yonkers, have both said they believed the state would need to raise additional revenue to deal with the fiscal crisis.

Republicans have said they oppose such increases, and business groups have warned that raising taxes on the wealthy could prompt some of them to leave the state. Mr. Cuomo’s budget director, Robert Mujica, has previously noted that about half of the state’s personal income tax revenue comes from the highest-earning 2% of taxpayers.

“New York is one of the highest taxed states in the nation, and raising taxes will result in the continuation of the exodus from this state,” Senate Minority Leader Robert Ortt, a Republican from Niagara County, said in a statement.

As Mr. Cuomo spoke in Albany, a group of progressive advocates unfurled a banner in Manhattan’s Central Park that represented the collective wealth of billionaires in the state. In addition to raising income-tax rates, groups like Make the Road New York, which works with undocumented immigrants, say the state should also tax financial transactions and the unrealized capital gains of high-wealth individuals.

Michael Kink, executive director of Strong Economy for All, a coalition of labor unions, said Mr. Cuomo should take an all-of-the-above approach to raising revenue before resorting to cuts.

“The governor has landed firmly in reality,” Mr. Kink said. “It’s absolutely true that tax hikes on the rich, on Wall Street and on big corporations are an essential part of any resolution to the budget crisis. We absolutely should not give up on federal funding, but we do need real relief now.”