The subway has long been a political football in part because of the unusual nature of its governance — even though it serves the city, it is controlled by the state, a fact that many riders do not realize. Mr. Cuomo and Mr. de Blasio spent months fighting over who should pay for the roughly $800 million subway rescue plan that was announced last summer after the governor declared a state of emergency for the system. Mr. de Blasio eventually agreed to pay for about half, but only under pressure from the state.

For his part, Mr. Byford assured reporters that he was up to the challenge. He said he was no stranger to a difficult political and media environment — Mr. Byford was in Toronto during the period when Rob Ford was that city’s combative mayor.

“I did my homework before I came here,” Mr. Byford said, acknowledging that New York City’s transit system was a hot potato. “I knew this would be a tough gig.”

Mr. Lhota said it was now the M.T.A.’s job to sell the plan to all levels of government. He joked that he was not a fan of the millionaire’s tax. “As somebody who would be subject to that tax,” he said, “I am not particularly interested.”

As Mr. Byford outlined the proposal, he compared the subway crisis to earlier emergencies that the city had confronted and recovered from, including the Sept. 11, 2001, terror attack and Hurricane Sandy.

“Not acting now is not an option, and it will only get more difficult and more expensive,” Mr. Byford said. “I believe this can be achieved and we now have a road map.”

As part of the plan, subway signals would be upgraded on lines that carry about three million people — or nearly half of the system’s ridership — in the first five years of the plan, which would start in 2019 or 2020. Rather than close entire lines on weekdays, the shutdowns would happen during nights and weekends and be contained to sections of lines. In the next five years, signals would be upgraded for another two million riders. Mr. Byford also proposed fixes to upgrade the floundering bus system and to improve accessibility for disabled riders.