With New York City’s transportation system in a state of crisis, the head of the Metropolitan Transportation Authority said on Thursday that it was time for City Hall to contribute more money to repairing and maintaining the subway system that is the lifeblood of the city.

In a hastily called news conference, Joseph J. Lhota, the newly named chairman of the M.T.A., said that he was preparing to submit an emergency plan to deal with the crisis and that he expected the city to offer financial assistance.

Mr. Lhota’s comments came on the heels of yet another acrimonious exchange between Gov. Andrew M. Cuomo and Mayor Bill de Blasio over the handling of the crisis.

The dispute revolved around both technical and legal aspects of the structure of the agency but really boiled down to a simple question: Should the city be contributing more money to the subway system’s well-being?