By Sebastien Malo

(Reuters) - Vice President Joe Biden, who last year compared New York's LaGuardia Airport to "some third-world country," on Monday was back in New York to tout a project that will rebuild it from the ground up.

"It's the greatest city in the world, and it requires a 21st-century infrastructure," Biden said at a news conference of the airport, which consistently ranks among the worst in the United States.

Biden and New York Governor Andrew Cuomo highlighted the role of Delta Air Lines Inc, the airport's biggest carrier, which has agreed to be a "full partner" in the redesign, said Cuomo.

An existing $3.6 billion public-private partnership is already under way to rebuild LaGuardia's Central Terminal, notorious to travelers for its leaky ceilings, threadbare atmosphere and meager food and public transit options.

It was not immediately clear what was new in the details Biden and Cuomo described. The governor's office did not reply to a request for clarification.

The plan calls for linking LaGuardia's new Central Terminal to Delta's Terminals C and D.

"We look forward to working in partnership with the governor’s design commission on a comprehensive and complementary redevelopment plan that realizes our mutual goals and benefits all New York passengers,” Delta's President Ed Bastian said in a news release.

The long-awaited overhaul of LaGuardia's Central Terminal took a leap forward in May when officials selected a Swedish builder consortium, Skanska AB's LaGuardia Gateway Partners, to design, build, operate and maintain the project.

Eight miles from midtown Manhattan, the closest airport to New York City handled nearly 27 million passengers in 2014, according to the Port Authority of New York and New Jersey, which runs it.

(Reporting by Sebastien Malo in New York; Additional reporting by Hilary Russ and Jeffrey Dastin; Editing by Cynthia Osterman)