With the December 22 deadline for applications fast approaching, only 1,240 death claims have been filed - a far cry from the 3,016 people known to have died in the attacks on the World Trade centre and the Pentagon, and in the Pennsylvania crash.

"I am concerned, and I think the administration is concerned," Kenneth Feinberg, the federally appointed lawyer who oversees the fund, told the New York Times. "The statute has a little more than three months to run. So where are the rest of the people?"

Families who apply to the fund, set up by Congress to protect airlines from litigation, waive their right to sue anybody else, apart from the terrorists who planned the attacks and those accused of harbouring or financing them.

Under a complex formula, each family receives a standard award for each dead relative, plus a top-up which is related to the victim's income and the consequent loss of projected family income. The average total award to date has been $1.6m (£1m).

It is not known why so few families have applied. Some are still believed to be too grief-stricken, while relatives of the 100 or so undocumented immigrants who are known to have perished may fear deportation, despite assurances that no sanction will be taken against them. Others complain of the huge amount of paperwork and the array of agencies and government bodies they need to deal with.

"Families are confused," said William Doyle, whose son Joey died in the attacks. "Between the court and the fund, there are a lot of deadlines."

But families who lost high-income earners are known to believe that the award is unfair, and have filed an unsuccessful lawsuit against the fund, demanding more money.

Many of them are believed to be awaiting court decisions pending against the airlines before making their move. "A lot of people would prefer to sue rather than go to the fund," said James Kriendler, an aviation disaster lawyer who represents many of the families. "But that really depends on your ability to tolerate risk."

If the courts decide that the airlines have some liability for people other than those who were in the aircraft, some families who lost high earners may choose to fight in the courts.

"If people want to litigate, fine," Mr Feinberg said. "I think it's a mistake, it's ineffective and protracted, and it prevents closure. But I really worry about the people who will arrive at December 22 having done nothing. Those people are united in their grief and fear, and they are the people I'm trying to reach."