At the centre of the inquiry is an army testing facility in Utah
Investigators suspect that a rogue scientist may have obtained access to samples of the bacteria.
The US says it is developing the sophisticated varieties of anthrax in order to test the effectiveness of vaccines, although critics say the programme may contravene an international treaty on biological weapons.
Over the last few weeks there have been several reports suggesting that the FBI's prime suspicions rest on a domestic source for the anthrax, although the bureau maintains publicly that it is keeping all options open.
According to the Washington Post newspaper, samples of the experimental anthrax have been sent regularly between an army production facility in Utah and an army test laboratory near Washington.
The paper has obtained shipping records which it says suggest that not all the anthrax has been accounted for.
Government programme
According to the US Government, the aim of the project is to reproduce a variety of anthrax developed by the Soviet bio-weapons programme in the 1980s.
Having re-created this virulent strain, they can then test vaccines against it.
Earlier this month a former UN biological weapons inspector told a US committee that the anthrax sent in the letters was of a higher grade than anything produced by the Soviet Union, by Iraq, or by the former US bio-weapons programme which officially finished in 1969.
The BBC's science correspondent, Richard Black, says most experts believe the current US programme is permitted by the 1972 treaty on biological weapons control, though some critics disagree, saying that the anthrax could be used offensively.
According to ABC News, citing federal authorities, the FBI is interviewing current and former scientists at the Utah facility, as well as at a private laboratory in Ohio run by the Battellie Memorial Institute - the other institution involved in the programme.
Some 200 US scientists dealt with the anthrax programme over the last five years, ABC said.
'Find a motive'
A leading expert in bio-terrorism, Barbara Hatch Rosenberg, who works as a molecular biologist at the State University of New York, has told the FBI the perpetrator probably has connections with the government.
"Many contractors work in government labs and would have access to material," said Ms Rosenberg.
She said the key to the investigation would probably involve finding someone with a motive, rather than further scientific analysis of the anthrax.
A day after the US Center for Disease and Control (CDC) announced that it would offer anthrax vaccinations or more antibiotics to thousands of people who were exposed to the disease during the mail attacks, the authorities are seeking to dispel confusion over who should consider them.
Authorities now say it is conceivable the spores could linger in the body for longer than after the 60 days of antibiotic therapy typically prescribed.
There are also concerns that the vaccine could have side effects.
CDC Director Dr Jeffrey Koplan told the AP news agency three groups of people should seriously consider the treatment: