The US News and World Report news magazine said on Friday in its online edition that the far-reaching programme covered more than 100 sites in the Washington DC, area and at least five other cities.
"In numerous cases, the monitoring required investigators to go on to the property under surveillance, although no search warrants or court orders were ever obtained, according to those with knowledge of the programme," the magazine said.
The report comes a week after revelations that the administration had authorised eavesdropping on people in the United States.
George Bush, the US president, has defended that covert programme and vowed to continue the practice, saying it was vital to protect the country.
Senior US officials, including Robert Mueller, director of the FBI, have repeatedly said Islamic militants appeared intent on acquiring weapons of mass destruction for an attack against the United States.
Mueller said in February he was "very concerned with the growing body of sensitive reporting that continues to show al-Qaida's clear intention to obtain and ultimately use some form of chemical, biological, radiological, nuclear or high-energy explosives material in its attacks against America".
"In numerous cases, the [FBI] monitoring required investigators to go on to the property under surveillance, although no search warrants or court orders were ever obtained"
US News and World Report
An FBI spokesman declined to confirm or deny the US News and World Report article and said: "We can't talk about a classified programme."
"The FBI's overriding priority is to prevent, disrupt and defeat terrorist operations in the US. All investigations and operations conducted by the FBI are intelligence driven and predicated on specific information about potential criminal acts or terrorist threats, and are conducted in strict conformance with federal law," he added.
The Council on American-Islamic Relations advocacy group said the report, coupled with news of the domestic eavesdropping, "could lead to the perception that we are no longer a nation ruled by law, but instead one in which fear trumps constitutional rights".
"All Americans should be concerned about the apparent trend toward a two-tiered system of justice, with full rights for most citizens, and another diminished set of rights for Muslims," it said in a statement.
Federal officials cited by US News and World Report maintained the programme was legal and said warrants were not needed for the kind of radiation sampling it conducted.
Officials also rejected any notion that the programme specifically targeted Muslims, the magazine said.
According to US News and World Report, the nuclear surveillance programme began in early 2002 and has been run by the FBI and the Department of Energy's Nuclear Emergency Support Team.
At its peak, the effort involved three vehicles in the Washington area monitoring 120 sites a day, nearly all of them Muslim targets such as prominent mosques and office buildings selected by the FBI, it said.
US Muslims have voiced concern
over the surveillance
The programme has also operated in at least five other cities - namely Chicago, Detroit, Las Vegas, New York, and Seattle - when threat levels there have risen, it said.
One source quoted by the magazine said the targets were almost all US citizens.