Officially they are saying nothing about who is suspected. But the word in political circles and in the press points more and more to the Saudi businessman Mr Osama bin Laden.
Indeed, officials could scarcely conceal their rage at the open leaking by Senator Orrin Hatch of details of a briefing by the security services to the Senate intelligence committee.
Mr Hatch told journalists that they had been briefed about intercepts by the CIA of radio communications involving bin Laden aides boasting after the attacks that they had hit two targets.
"We happened to know just today that we have information that indicates representatives that are affiliated with Osama bin Laden were actually saying over the airwaves, private airwaves, that they had hit two targets," Mr Hatch told reporters.
One intelligence official, however, told the New York Times that the information was not quite as unambiguous as that. "It is not definitive, but there certainly are a lot of indicators pointing at bin Laden," he said.
The German, French, British and Israeli secret services also share that view, a senior German government official said yesterday.
"The way it was carried out, the choice of targets, the military approach, the highly professional preparation and the presumably large financial resources ... (all) mean there are many points that indicate we should look for the perpetrators among those around Osama bin Laden," Chancellor Gerhard Schr÷der's chief of staff Mr Frank-Walter Steinmeier said.
The four intelligence services were all in agreement, he said, adding that Germany expected the United States to retaliate for the attacks.
Mr bin Laden (44), an extremist Islamic militant from a wealthy Saudi family, has been defying US efforts to capture or kill him for years. Since 1996, he has been living under the protection of the fundamentalist Taliban regime in Afghanistan in a remote mountain hideout. He has previously been linked to terrorists who attempted to destroy the World Trade Centre in 1993.
He has also been indicted for the deadly 1998 bombings of the US embassies in Dar es Salaam, Tanzania, and Nairobi and was linked to last October's attack on the USS Cole in Aden, Yemen, which killed 17 American servicemen.
A videotape has been circulating in the Middle East for several months in which Mr bin Laden recites a victory poem about the Cole bombing, then issues a call to arms: "To all the Mujah: your brothers in Palestine are waiting for you; it's time to penetrate America and Israel and hit them where it hurts them most." The attacks on the US came one day before a bin Laden associate was due to be sentenced in New York for his role in the Tanzanian bombing. The federal courthouse is in lower Manhattan, near the World Trade Centre.
US spending on counter-terrorism in the last few years has doubled from $6 billion in 1995 to $12 billion this year, but its focus has been largely external.
Unprecedented in scope and sophistication, the co-ordinated assault on the world's financial and political capitals caught the United States completely off guard - despite a massive intelligence and law enforcement network devoted to detecting and thwarting such attacks. With efforts focused largely on guarding against bomb threats to overseas targets, US authorities conceded they were ill-prepared for hijacked airliners purposely crashed on American soil.
Crucially they lacked the traditional intelligence sources from agents infiltrated into the terrorist groups.
That has led to serious questioning of 1995 rules which tie the hands of the CIA over the use of human intelligence. Nervous about how it would look in Congress if US money ended up subsidising terrorist groups, the organisation has been forced to severely curtail its direct contacts.
Now several members of the Senate committee are demanding changes, while a former head of the CIA is openly campaigning for a repeal of the rules.
Huge deficiencies in airport security systems have also been the focus of much criticism here. Study after study has shown up weaknesses, but complacency has been the order of the day. When the Department of Transportation tried to breach security at eight airports three years ago they succeeded 68 per cent of the time. Logan Airport in Boston, from which two of the flights left, has been particularly bad, with 136 citations for security violations from 1997 to 1999, for which its authorities were fined $178,000.
The result is likely to be a belated clampdown with inevitable delays for passengers.
Some 2 million passengers depart every day from 460 airports in the US.
