British sources point out that despite extensive inquiries, no evidence has been produced to show that he had access to the radioactive material needed to build the bomb, or indeed that he had even worked out a time or place to launch the attack.
The most that could be said about Mr Muhajir, a former member of a Chicago street gang now allegedly working for al-Qa'ida, is that he had the "intention" of launching such an attack, security sources said.
President Bush announced yesterday that a "full-scale manhunt" was under way across the United States for accomplices of Mr Muhajir. "We will run down every lead, every hint. We're in for a long struggle in this war on terror. And there are people that still want to harm America."
Before his arrest at Chicago's O'Hare airport on 8 May, Mr Muhajir - who changed his name from Jose Padilla - stopped in Zurich on the way from Pakistan, where he collected $10,500 (£7,000).
Despite claims by the Attorney General, John Ashcroft, that the FBI had disrupted a plan to launch a radioactive attack against Washington, other officials conceded yesterday that there was no evidence that any such plot had progressed beyond the most basic stages.
British security sources, who believe Mr Muhajir might have been acting as a courier, said the Americans investigated Mr Muhajir's activities and tried to find a terrorist network he may have been involved with inside the US. The highly publicised announcement of the arrest only came after the failure to find anything more incriminating.
In Washington there was a growing suspicion that the arrest was seized on by the Bush administration in dramatic fashion for political ends. British and European security agencies do believe, however, that there is still a real threat of a possible attack.