He did not elaborate on what measures would be taken, but he said in a subsequent radio interview on WCBS that the Metropolitan Transportation Authority, which runs the subways, needed to “take dramatic action and they have to take it now.”

Mr. Cuomo called on the authority, which he effectively controls, to tell him what steps needed to be taken.

Tensions between City Hall and the authority over what to do about homeless people sleeping on trains and in stations had been building long before the virus outbreak hit the city.

As subway ridership has plummeted during the ensuing shutdown, there is some evidence that more homeless people are using largely empty trains for sleeping.

Advocates for homeless people said that many of them have avoided dormitory-style city shelters where the virus has spread rapidly and killed dozens of people.

On Monday, Mayor Bill de Blasio said the city would increase outreach efforts for homeless people at subway stations and provide 200 more shelter beds. He also asked the authority to temporarily close 10 end-of-the-line stations from midnight to 5 a.m. so workers could offer services to riders leaving trains and do “enhanced sanitization” of subway cars.

Sarah Feinberg, the interim president of New York City Transit, which operates the city’s subway and buses, said in a radio interview on Tuesday that she welcomed the mayor’s announcement but suggested it would not go far enough.