The Associated Press reports 30 governors in all have received the letter, promoting a warning an investigation by the FBI.
The letters from a group calling itself Guardians of the Free Republics demand that the governors leave office within three days or they will be removed.
While investigators do not see threats of violence in the letters, a federal intelligence note is warning police the calls may encourage others to act out violently.
"In this case, it does not appear to be a threat. It really is more an expression of First Amendment rights," FBI Special Agent in Charge Jim Davis said.
"As long as that's where this stays, we have no interest in this group. If it moves beyond that then they will receive a lot of interest from us," Steve Olson, also of the FBI, said.
The warning comes as law enforcement officials pay more attention to far-right extremist groups after the arrest of nine Christian militia members last weekend accused of plotting violence.
Guardians of the Free Republics says on its Web site that it wants to "restore America" by peacefully dismantling parts of the government.
(KUSA-TV © 2010 Multimedia Holdings Corporation with The Associated Press)