“It’s refreshing to see someone stand before the people,” Mr. Lhota said, “and say, ‘Hold me responsible. Hold me accountable.’”

Mr. Johnson’s speech had the feel of a campaign rally as he sought to position himself as a leader capable of thinking big, in contrast to Mr. de Blasio, who has been criticized for a lack of bold new initiatives in his second term. Mr. Johnson also challenged the state Legislature, saying that the City Council would approve congestion pricing if Albany failed to do so, though it is not clear whether the Council has the authority.

The speech made clear that if Mr. Johnson runs for mayor, he would use the city takeover of the transit system as a signature issue, just as Mr. de Blasio focused on early childhood education when he first ran for mayor in 2013. Mr. Johnson was introduced by his mother, Ann Richardson, who is from Boston and has the accent to match, telling the audience about her son’s “kind loving haht.”

Mr. Cuomo, a Democrat in his third term, has received a wave of criticism over his handling of the transit system. Although he exerts great control over the agency, he has argued that he does not have enough power and that one person or entity should take charge and be accountable to the public.

A Cuomo spokeswoman, Dani Lever, responded to Mr. Johnson’s speech with a short retort: “The city already owns the New York City Transit system,” in reference to a long-running debate over whether the city technically owns the system — a contention that Mr. de Blasio’s office has disputed.

The authority is governed by a board that typically has 17 voting members, including six members chosen by the governor and four by New York’s mayor. Mr. Cuomo selects the board chairman and has a role in hiring the agency’s top leadership.

Mr. Johnson was careful not to mention Mr. Cuomo’s name or to attack him directly, though he criticized the unpopular decision by the Cuomo administration to divert transit funding to struggling ski resorts. Mr. Johnson joked that a mayor would never make that decision over fears that it would lead to tabloid headlines of “Mayor to City: Go Sled!”