Deputy Chief of Staff Lynn Hettrick said the FBI told administration officials a few days ago that several governors have received letters from what he described as a sovereign citizens group.
The letter reportedly tells governors to resign and take a new oath to a new order, and that members would "commandeer" state offices the state chief executives did not step down.
"The FBI informed us the letter would be coming," Hettrick said. "It came here and it was confiscated for evidence."
Hettrick said there was no specific threat of violence but extra security was installed as a precaution. He wouldn't divulge details of the letter but said the group claimed to be nonviolent.
"We're not really overly concerned, but at the same time we don't want to sit back and do nothing and regret it," Hettrick said.
A metal detector and X-ray machine to screen visitors and packages were placed at the building's main entrance, and other entrances have been closed.
FBI spokesman Joe Dickey in Las Vegas confirmed Gibbons received a letter, but said he couldn't comment further.
The Nevada Capitol in the heart of Carson City was finished in 1871. It houses offices for five state constitutional officers — the governor, lieutenant governor, secretary of state, treasurer and controller.

