A US federal jury has begun hearing a case to decide whether the leaseholder of the World Trade Center can claim insurance for one attack or two.
The case could have an impact on rebuilding on the site
Developer Larry Silverstein wants insurance firms to pay out for two attacks on 11 September, 2001.
The insurance companies dispute the claim, saying the attacks on the twin towers amounted to a single event.
Mr Silverstein would receive $7bn for two attacks, as opposed to $3bn if the attacks are classified as one.
The property magnate says the attacks were two events because the hijacked aircraft hit the World Trade Center 15 minutes apart.
A larger payout will enable Mr Silverstein to build a new tower, skyscrapers and other buildings on Ground Zero within the next decade.
The smaller figure could mean years of delays.
"Anyone who's in New York knows that how much we recover from this lawsuit will have an impact on the rebuilding of this site," said Kevin M Rampe, president of the Lower Manhattan Development Corporation.
Mr Silverstein, who owned the leasehold on the World Trade Center, suffered a setback last September, when a federal appeals court defined the destruction as one event but ruled a jury should decide the case.
There is also the complication of the fact that while the leasehold was signed months before the 9/11 attacks, the insurance contracts had not been formally written.