Katie Hobbs, the Democratic secretary of state in Arizona, who gained national attention for her stalwart defense of the state’s electoral system in the aftermath of the 2020 presidential election, announced on Wednesday that she was running for governor, portraying herself as a pragmatic leader who does not back down in the face of criticism and threats.

Ms. Hobbs has become a frequent fixture on cable news shows since the fall — first as Arizona’s vote count continued for several days after Election Day in November, and again this spring as Republicans conducted a widely criticized audit of ballots cast in Maricopa County. Ms. Hobbs has repeatedly condemned the partisan recount as a dangerous threat to democracy and has assigned observers to track problems with the process.

“We did our job,” she said in a video announcing her bid. “They refused to do theirs. And there’s a lot more work to be done.”

In some ways, the recount has elevated Ms. Hobbs, who some polls suggest is the most popular statewide elected official. She joined a lawsuit to try to stop the recount, which has no official standing and will not change the state’s vote. She issued a scathing six-page letter detailing problems with the audit and has recommended that Maricopa County replace its voting machines and vote tabulators because of the lack of physical security and transparency around the process. “We cannot be certain who accessed the voting equipment and what might have been done to them,” she wrote.

A campaign video announcing her run opens by referring to the attacks and death threats that she has faced in the wake of the election — including armed protesters showing up at her home.

“When you’re under attack, some would have you believe you have two choices: fight or give in. But there is a third option: get the job done,” Ms. Hobbs says in the video announcement. “I’m here to solve problems.”

In the days after last November’s election, as Arizona’s votes were being counted amid intense scrutiny and criticism from the Trump White House and its allies, Ms. Hobbs regularly appeared on television to provide updates on the counting process and defend the integrity of the state’s voting processes.

Republicans in the State Legislature have struck back at Ms. Hobbs for her opposition to the recount. After Ms. Hobbs sued them, Republicans passed a measure to strip her of her ability to defend election lawsuits, instead giving that power to the attorney general, also a Republican.

The bill, which has not yet been approved by the full Legislature, appears to specifically target Ms. Hobbs; it would expire in January of 2023, when her current term ends. Ms. Hobbs called the measure “an attack on Arizona voters.”

The Arizona G.O.P. has largely doubled down on the baseless accusation that the election was “stolen” from former President Donald J. Trump, with the state party going as far as censuring elected officials, including the Republican governor, Doug Ducey, for not being sufficiently loyal by declining to back the attempt to subvert the election.

But the efforts have largely turned off independent voters in the state, who make up roughly a third of the electorate there.

“The other side isn’t offering policies to make our lives better, they’re offering conspiracy theories that only make our lives worse,” Ms. Hobbs said in her video.

Mr. Ducey is not eligible to run in the 2022 election because of term limits and the field to replace him is likely to be crowded. Several Republicans have also declared their candidacy in recent days, including Kimberly Yee, who is currently the state treasurer, and Kari Lake, a former anchor for the local Fox television station.