Attacks have targeted the US Government and media
In a rare glimpse into the investigation, agents say they have built up a psychological and linguistic profile of the culprit.
The announcement came as President George W Bush ordered security to be beefed up at airports for the holiday season, which begins with Thanksgiving on 22 November.
Tom Ridge, the US homeland security director, said on Wednesday he was "hopeful" that the anthrax outbreaks were over but another four postal facilities in New Jersey have since tested positive for the disease.
The FBI say they have not ruled out links with a terrorist organisation, but behavioural and linguistic evidence points to - as they put it - an opportunist of domestic origin.
At least three letters containing anthrax spores have been sent since the 11 September attacks on New York and Washington. Four people have died, two of them postal workers.
Inexpensive equipment
The letters were posted on 18 September and 9 October.
The FBI say the suspect is probably an adult male who may have referred to the US attacks in his messages only as a decoy.
He may have no more scientific knowledge than a lab technician and his equipment need not have cost more than $2,500.
He could have set it up in his garage, or in his attic.
He is, agents believe, a loner, someone not given to face-to-face confrontation, nor, as they put it, to speeding through stop signs. He is rational and methodical but "lacks the personal skills necessary to confront others".
BBC Washington correspondent Tim Franks says the FBI hopes that its detailed analysis of the culprit will prompt a friend or relative to tip them off.
The latest contaminated post offices - named as Palmer Square, Rocky Hill, Trenton Station E and Jackson - all send mail to a sorting centre which handled letters containing anthrax spores sent to Washington and New York.
Extra security
US Postal Service spokesman Bob Anderson, who confirmed the finds, did not specify their origin or how fresh they were.
About 20 US post offices have tested positive for anthrax and thousands of postal workers have been put on preventive antibiotics since the outbreak began.
On Friday, President Bush ordered America's states to put an additional 2,000 National Guardsmen on guard at airports for the Thanksgiving/Christmas holiday period.
He confirmed that 6,000 guardsmen had already been deployed at airports since the 11 September attacks.
Their duties include monitoring passengers and screening baggage, as well as guarding airport facilities.
"This increase in security will last through the busy holiday period ... and we believe they'll help a lot," said Mr Bush.
In another development, America's largest airport security company, Atlanta-based Argenbright, announced it was tightening its own procedures, including checks on staff.