An 80-story skyscraper under construction at ground zero will have to stop at seven stories unless the developer can line up more tenants, planners said Monday, adding to problems that have plagued the $11.7 billion World Trade Center project.

Silverstein Properties Inc. said it is still looking for tenants to fill the first 10 floors of Three World Trade Center, the third-highest building in the planned office complex. Without those leases, the Port Authority of New York and New Jersey will not guarantee the financing that Silverstein needs to finish the building.

Construction would end at the so-called "podium" level on the seventh floor, with the option of building up later on, and the floors below would be filled mainly with retail stores.

Many companies in New York are reluctant to invest in new offices because of the poor economy, and dozens are negotiating lower rents as five-year leases signed before the housing crash begin to expire. But both Silverstein and the Port Authority said they are confident the developer can get enough tenants lined up.

"We are currently speaking with a number of potential tenants and remain fully optimistic that we will sign a lease in time to complete the tower as scheduled in 2015," Larry Silverstein, the company's chief executive, said in a written statement.

Mayor Michael Bloomberg said that he would be disappointed if Three World Trade did not go higher, but that the city would not extend any aid to keep it going. The most important part of the project, he said, is laying the infrastructure for future construction.

"If you did that and you couldn't keep building up, I think that's a shame," Bloomberg told reporters. "But there are things that should depend on the marketplace and investors. That should be up to them."

The 10-story "pre-lease" requirement is included in a 2010 agreement between Silverstein and the Port Authority. The difficulty in finding tenants comes amid other problems that have dogged the project.

Work on a museum at ground zero has stopped because of a dispute between the Port Authority and the National September 11 Memorial & Museum over who should pay for infrastructure costs. The Port Authority says the foundation owes it $300 million, while the foundation says the price tag should be closer to $140 million.

Planners had hoped to open the museum on the 11th anniversary of the 2001 terrorist attacks, but Bloomberg has said that's no longer possible.

Work has also slowed on One World Trade Center, the spire formerly known as the Freedom Tower. Workers had been averaging a floor a week in mid-2011, but photographs have shown little growth in recent months.

The Port Authority's executive director, Patrick Foye, blamed rainy weather and high winds at the top of the building, which is now 90 stories high. He spoke to reporters following a panel discussion on infrastructure at Fordham University.

The authority also says it is having trouble finding space for the trailers that move upward with the workers. As the tower narrows, there is less space on each floor, and transferring the trailers upward takes more time.

DCM Erectors, the New York-based company that is laying the steel, has also had financial problems, Foye confirmed Monday. He said the authority has had to step in and pay some of the company's bills.

Steel deliveries have continued, he said.

"They have made arrangements with their financing sources," Foye said. "The thing that's important to us is they continue to fabricate steel and deliver it, and we continue to install it."

DCM did not immediately return a telephone call seeking comment.

Foye said that One World Trade Center is 60 percent leased and that the authority is still aiming for a completion date in the fourth quarter of 2013.

The Port Authority is also fighting a lawsuit filed by AAA, the motorists' club, over its decision to raise bridge and tunnel tolls in September. The Port Authority said it needed the extra revenue to improve its creditworthiness, allowing it to borrow money more cheaply for projects like the World Trade Center.

After the toll hike, the governors of New York and New Jersey ordered a review of the Port Authority's finances. The Port Authority plans to release the first results of that review before the end of the month, Foye said.

"It's going to be a foundation and a platform for reform of the Port Authority and growth going forward," Foye said. He would not elaborate.

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