Mr. Cuomo pushed for $2.5 billion in the capital plan for improvements at the New York airports, possibly including an AirTrain link from New York City’s subway system to La Guardia. Mr. Cuomo’s advisory panel suggested that most of the rest of the money — up to $7 billion — could come from private sources, including airlines that use J.F.K.

Kennedy is a collection of free-standing terminals, some of which were built, at least in part, by the airlines that occupy them. JetBlue Airways and the authority split the cost of building Terminal 5, which opened in 2008. Delta Air Lines has spent more than $1 billion in the recent years to improve its facilities at Terminals 2 and 4.

At La Guardia, the authority has committed $600 million to the rebuilding of Terminals C and D against an estimated cost of about $4 billion. That investment would come on top of a $4 billion rebuilding of the Central Terminal Building there, which began last year.

Mr. Cuomo hopes to entice airlines to make similar investments at J.F.K. to compete for customers. He challenged airlines to make offers, saying Delta had called him at 5:45 a.m. on Wednesday.

Mr. Cuomo did not mention seeking federal financing. President-elect Donald J. Trump has said he plans to make an ambitious investment in infrastructure a priority of his administration.

As part of Mr. Cuomo’s plan for J.F.K., Matthew Driscoll, New York State’s transportation commissioner, said his agency would spend as much as $2 billion to improve the flow of traffic to and from the airport. The changes would include adding a lane to the Van Wyck Expressway and widening ramps at the busy interchange in Kew Gardens, Queens, which Mr. Driscoll said handles 250,000 vehicles per day.

Thomas F. Prendergast, chairman of the Metropolitan Transportation Authority, said that transit agencies would explore creating a one-seat ride between Manhattan and J.F.K. Travelers must now switch to the AirTrain from the subway or Long Island Rail Road, a transfer that Mr. Prendergast described as “schlepping with your luggage.”

Though New York City owns the land under J.F.K., no one from City Hall attended Mr. Cuomo’s speech. “Investments in New York City’s airports are vitally important to our region’s long-term development,” said Melissa Grace, a spokeswoman for Mayor Bill de Blasio. “We look forward to hearing more details about the plans for J.F.K. in the months to come.”