Government spokeswoman Yusill Scribner said she had no immediate comment on the lawsuits.
FBI spokesman Richard Kolko said the agency had not reviewed the lawsuit against it and would not comment on pending litigation.
A victims' compensation fund established by Congress has paid $6 billion (€4.35 billion) to 2,880 families of those who died in the attacks and more than $1 billion (€720 million) to 2,680 injured victims.
But 41 cases filed on behalf of 42 victims remain pending in federal court in Manhattan because some victims decided to pursue the usual court route rather than accept payouts from the September 11th Victim Compensation Fund of 2001.
The first trials to assess damages are scheduled to begin in September.