Directors of the Global Gateway Alliance, a group of business leaders that advocates improved airports, sent a letter last month to Port Authority officials, saying it was “time to come to a conclusion, choose a developer and get the project started.”

The alliance’s chairman, Joseph J. Sitt, is pressing the Port Authority to move forward with a plan to add a hotel at Kennedy and to improve the transit links to each of the major airports. The Port Authority has $1.2 billion in its capital plan for an extension of the PATH train to Newark Liberty, a project that is a favorite of New Jersey’s governor, Chris Christie.

In a statement, Patrick J. Foye, the executive director of the Port Authority, said the agency, “at Governor Cuomo’s direction, is conducting design competitions to re-envision New York’s John F. Kennedy and LaGuardia Airports for the 21st century.” Mr. Foye said that “billion-dollar-plus investments” by Delta and JetBlue had “created beautiful, state-of-the-art terminals” at Kennedy and La Guardia.

Still, he added, “much more remains to be done to achieve Governor Cuomo’s goals for the airports.”

The most intractable obstacle to improving air travel in the metropolitan area is the congested airspace. The bulk of the air travel delays in the nation emanate from the New York area, and the three airports regularly rank among the worst in the nation in on-time performance. That problem will not be fixed without a switch from an air traffic control system that relies on radar beacons to one guided by satellites.

Some airlines, including Delta, JetBlue and United, have plowed ahead with overhauls of their terminals that have cost more than $3 billion.

At La Guardia, Delta is remaking Terminal C in the image of its longtime home there, Terminal D. The corridors are filled with bar-height seating, and counters are crowned with tablets that customers can use to order food and drinks, check on their flights and amuse themselves.

“Hip and cool” is the “vibe” Delta is trying to achieve in its New York terminals, said Gail A. Grimmett, a senior vice president who oversees the airline’s operations in the city. She said the changes Delta made at La Guardia had reduced “gate anxiety” and brought a calmer, more comfortable atmosphere to the terminals.