NEW YORK (AP) A meeting aimed at resolving an impasse over who will pay for new office towers at the World Trade Center site resulted only with an agreement by top elected officials from New York and New Jersey to meet in June with the developer.

New York City Mayor Michael Bloomberg told reporters after May 21’s meeting with other officials and developer Larry Silverstein that the next meeting will be June 11.

“I think we all agree that further delay of the World Trade Center is simply not acceptable,’’ Bloomberg said.

The mayor said the officials and Silverstein each agreed to “put people that really speak for us in a room, lock the door figuratively for the next few weeks and let them come up with a solution to the problem.’’

Bloomberg added, “We do have a duty to make lower Manhattan whole again.’’

Besides Bloomberg and Silverstein, participants included New York Gov. David Paterson, New Jersey Gov. Jon Corzine, New York State Assembly Speaker Sheldon Silver and officials from the Port Authority of New York and New Jersey, which owns the land.

“I felt renewed vigor in the room with all the parties talking and cooperating,’’ Patterson said.

“Both sides have committed to moving forward and trying to accommodate the others’ position,’’ Silverstein added.

The developer is trying to renegotiate his lease to build three of five office towers to replace the destroyed World Trade Center. Silverstein is having difficulty finding financing for the towers in the current real estate market and wants the Port Authority to back at least two of the buildings.

The Port Authority said it will back one tower with about $800 million in return for Silverstein investing additional money in building the infrastructure at the World Trade Center site, which includes the office towers, a public transportation hub and the Sept. 11 memorial.

The Port Authority has said it would not be realistic to build the five planned office towers in the current real estate market and has suggested waiting until the market rebounds.

Kathryn Wylde, president of the Partnership for New York City, a business group, applauded the mayor for bringing together the key parties to discuss the future of the World Trade Center site.

“It is crucial to the future of the city’s economy that this issue be resolved swiftly and amicably,’’ she said.

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