NEW YORK — A year after comparing New York’s LaGuardia Airport to “some Third World country,” Vice President Joe Biden helped unveil an ambitious plan Monday to rebuild its collection of aging terminals into a modern, unified hub while easing congestion by doubling the space available for planes to operate.

“I wish everything I said that was truthful but controversial would turn out this well,” he joked during the announcement with New York Gov. Andrew Cuomo.

The overhaul would remake the entire footprint of the airport, which is shoehorned onto a small, oddly shaped property on the shore of the East River.

Its existing, cramped and chaotic buildings would be demolished and replaced with a big new terminal 600 feet closer to the Grand Central Parkway, the highway that rings the airport like a moat.

That shift would relieve some of the space constraints for aircraft trying to taxi to and from the congested gate areas. More space would be made by having passengers get to their gates using elevated passageways that pass over active taxiways. In all, nearly two miles of new taxiways would be created.

Construction on the first phase of the project would begin next year, pending final approval by the Port Authority of New York and New Jersey, which owns the airport. A second phase would be overseen by Delta Air Lines.

The first remade portions of the airport would open to passengers in 2019.

“This is what New Yorkers deserve and have deserved for a long time. And now we’re going to get it,” Cuomo said.

He said the current airport is a collection of cramped terminals with high volume and low ceilings, and is “un-New York.”

“It’s slow, it’s dated, it has a terrible front-door entrance way to New York,” he said.

Biden said last year that if he blindfolded someone and took him to LaGuardia, he’d think he was in “some Third World country.” Biden lauded the governor for “thinking big.”

The vice president’s influence was critical, Cuomo said – approvals that would normally take years were expedited by Biden’s office.

The first phase of the plan will cost $4 billion, half from private funding, Cuomo said. Delta is a partner in the new terminal.

The new airport is part of an ambitious plan aimed at four of the state’s airports in the New York area. Stewart Airport north of the city and Republic Airport on Long Island would both get Startup New York designation, offering new and expanding businesses to operate tax free for 10 years. Also, New York City’s John F. Kennedy Airport would have its architecturally distinct Saarinen building reconfigured into a hotel.

The construction will add thousands of jobs and help grow tourism and commerce. Officials said it would triple the screening space, create better connections between terminals, and more.