A Republican county clerk in Colorado who was stripped of her responsibility of overseeing county elections is joining a growing movement of people throughout the country who spread false claims about fraud in the 2020 presidential election and want to oversee the next one.

Tina Peters, the Mesa County clerk, who is facing accusations that she breached the security of voting machines, announced on Monday that she would run to be the top elections official in Colorado.

At least three Republicans challengers are already running to unseat the current Colorado secretary of state, Jena Griswold, a Democrat.

Colorado is a purple state that President Biden won with 55 percent of the vote in 2020. The state’s primary is on June 28, and Colorado is one of 27 states whose top elections official will be on the ballot this year.

In 2020, when former President Donald J. Trump and his allies sought to undo the results of the election, they focused their pressure campaign on these relatively little-known officeholders.

“I am the wall between your vote and nationalized elections,” Ms. Peters said during an appearance Monday on a podcast hosted by Stephen K. Bannon, the embattled former top aide to Mr. Trump. “They are coming after me because I am standing in their way — of truth, transparency and elections held closest to the people.”

Ms. Griswold, who is also the head of the Democratic Association of Secretaries of State, said in a statement on Monday that Ms. Peters was “unfit to be secretary of state and a danger to Colorado elections,” citing Ms. Peters’s attempts to discredit the results of the 2020 presidential election.

Ms. Peters did not immediately respond to telephone and email messages on Monday seeking comment.

Elected in 2018, Ms. Peters took office as clerk and recorder of Mesa County, in far western Colorado, in 2019. By late 2021 a Mesa County Court judge had upheld Ms. Griswold’s removing Ms. Peters from overseeing elections in the county and replacing her with an appointee.

In May of last year, Ms. Peters and two other people entered a secure area of a warehouse in Mesa County where crucial election information was stored. They copied hard drives and election-management software from voting machines, the authorities said.

In early August, the conservative website Gateway Pundit posted passwords for the county’s election machines. In October Ms. Peters spoke at a gathering in South Dakota of people determined to show that the 2020 election had been stolen from Mr. Trump.

The gathering also featured a large screen that, at one point, showed the software from the election machines in Mesa County.

Ms. Griswold said her office had concluded that the passwords leaked out when Ms. Peters enlisted a staff member to accompany her to surreptitiously record a routine voting-machine maintenance procedure. State and county officials announced last month that a grand jury was looking into allegations of tampering with Mesa County election equipment and “official misconduct.”

More recently, Ms. Peters was briefly detained by the police when she obstructed efforts by officials with the local district attorney to serve a search warrant for her iPad. Ms. Peters may have used the iPad to record a court proceeding related to one of her deputies, according to Stephanie Reecy, a spokeswoman for the county.

In video of the Feb. 8 encounter, taken by a bystander and posted on Twitter, Ms. Peters can be heard repeatedly saying, “Let go of me,” as officers seek to detain her. “It hurts. Let go of me,” she says, before bending her leg and raising her foot toward the officer standing behind her.

An officer responds, “Do not kick,” according to body camera video posted by KJCT News 8, a local station. “Do you understand?”

Ms. Peters was charged with obstructing a peace officer and obstructing government operations, according to the Mesa County Sheriff’s Office. She turned herself in to the authorities on Thursday, posted $500 bond and was released, according to county officials.

“I still have the bruises on my arm where they manhandled me,” Ms. Peters told Mr. Bannon on Monday. Later she said: “I just want to say I love the people. That’s why I’m doing this.”

Mr. Bannon said Ms. Peters had been targeted because of her fight against “this globalist apparatus.”

“Thank you,” Ms. Peters told the host. “I’ll work hard for you guys.”