World Trade Centre leaseholder Larry Silverstein has filed a lawsuit, declaring that his $1bn (£623m) liability policy issued by Zurich, protects the owners of the complex.
He has asked a federal judge to rule that the policy also provides protection for the Port Authority of New York and New Jersey.
Zurich American has filed a counter suit, asking the US judge to limit its liability to Silverstein.
Silverstein issued a statement, saying he is seeking a ruling that Zurich is "obliged to provide" coverage to the Port Authority.