Mr. Cuomo had suggested earlier in the week that the city had a surplus from which it could draw much more, a characterization that a City Hall spokeswoman contested.

“I didn’t know the M.T.A. was a city authority,” the spokeswoman, Amy Spitalnick, wrote on Twitter on Wednesday in response to the governor’s comments. “Do they want to give us control? Please?”

This was not exactly a formal request. Unlike some of his competitors in the 2013 race for mayor, Mr. de Blasio, a Democrat, has not called for the city to take control of the transportation authority.

It remained unclear on Friday where any additional city money might come from. The de Blasio administration said the state’s request for $3.2 billion over five years would amount to more than 10 percent of what the city would typically spend on capital projects over the same period.

The governor said that the transportation authority, whose chairman he selected, had been responsible for determining the proper spending levels for the state and the city under the plan.

“I could argue that it’s a little burdensome on the state,” he said. “But I would accept the M.T.A.’s numbers just to get it done and to go forward.”

City officials have suggested that they would be open to increasing their funding under the right circumstances — in exchange, presumably, for greater influence over how the money is spent.