The relatives accuse the fund's administrator, Kenneth Feinberg, of being autocratic, arrogant and having "alienated and disenfranchised the very constituency he was appointed to serve".

All the families involved in the lawsuit are related to victims who worked for the stockbroking firm Cantor Fitzgerald. They claim the fund has put an illegal cap on the awards, which will leave some high-income families with just 10% of the sum to which they are entitled.

The lawsuit further contends that the fund discriminates against unmarried victims, and violates New York law by calculating the awards on the basis of after-tax projections of lost income.

One widow, quoted in the New York Times, said: "My husband worked a second job to support our children and me, and now he's gone. The amount of money we'll get if Feinberg's rules stay the way they are now is unfair. The simple fact is that we need more help."

The changes in the rules and formulas governing the administration of the fund demanded in the suit could increase payments made by the fund to billions of dollars more than the $4bn-5bn already envisaged.

The annual salaries of the plaintiffs range from less than $50,000 (£30,000) to $1m (£600,000). Mr Feinberg would also have to reassess 154 payments already made to families, which average $1.56m.

"It's not his job to balance the budget or bring this project in under a certain number," said John Cambria, the families' lawyer. "It's his job to carry out this statue passed by Congress."

Legal experts say that while the plaintiffs' case is strong, it may still not succeed.

Pamela Falk, a professor at the City University of New York, said: "The court will have to weigh a strong and sympathetic case by the victims that they have not been fairly compensated against a longstanding tradition in US law to give deference to government administrators."

Mr Feinberg, who has 60 days to respond to the lawsuit, told the New York Times he knew nothing about it.