Mr. Cuomo, a Democrat and a source of speculation about a possible run for president in 2020, had received criticism for remaining mostly silent over the city’s subway meltdowns. He controls the Metropolitan Transportation Authority, the agency that runs the subways and the Long Island Rail Road, which will also suffer delays at Penn Station this summer.

Mr. Cuomo proposed a series of ambitious ideas: New York State should consider taking over Penn Station, or the station should be run by a private operator, or by the Port Authority of New York and New Jersey. As it happens, the Port Authority runs the one transit hub, the main bus terminal in Manhattan, that many travelers find at least as unappealing as Penn Station.

Mr. Cuomo also announced an international competition to solicit ideas about how the subway could run more trains and buy new cars more quickly. Winning proposals would earn a $1 million prize. And Mr. Cuomo said that if the authority needed more money for its five-year capital plan to address subway delays, he would help fight for it at the state and local levels, even though as governor he already has a lot of power over the state’s finances.

An array of elected officials joined Mr. Cuomo onstage and praised his plans, including John J. Flanagan, the Republican State Senate leader, and Melissa Mark-Viverito, the Democratic leader of the New York City Council. Noticeably missing was Mayor Bill de Blasio, a frequent nemesis of the governor, although the city’s transportation commissioner, Polly Trottenberg, did attend.

Some transit advocates have called on Mr. Cuomo and Mr. de Blasio to work together to fix the subway. But Mr. de Blasio, a Democrat, slammed Mr. Cuomo last week, saying that Mr. Cuomo ran the subways and should “just own up to it.”

After Tuesday’s speech, Ms. Trottenberg, who also serves on the authority’s board, struck a softer tone. “The city is obviously interested in being part of the discussions and being helpful,” she said. “This is all our constituents. We want to make sure they can all have a great transportation system.”

John Raskin, the executive director of the Riders Alliance, an advocacy group that has criticized Mr. Cuomo’s leadership of the authority, welcomed the governor’s attention to the problems.