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Democratic incumbent Raphael Warnock kicked off his Georgia Senate runoff bid Thursday by tearing into Republican Herschel Walker, telling a crowd in Atlanta that his opponent has a "disturbing history pattern of violence against women" and "against his own family."

Warnock appeared to be referencing a claim from Walker’s ex-girlfriend that he allegedly threatened her life in 2012, which the Republican’s campaign has called "baseless."

"We've seen that Herschel Walker has a disturbing history pattern of violence against women, against his own family. And he takes and he refuses to take responsibility for that," Warnock said Thursday. "And he refuses even to answer questions. So, the question right now is this: is that who we want representing Georgia?"

The runoff between Warnock and Walker is scheduled for Dec. 6 after neither candidate captured 50% of the vote in Tuesday’s midterm election.

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Democratic Georgia Sen. Raphael Warnock speaks on election night

Democratic Sen. Raphael Warnock speaks during an election-night watch party in Atlanta, Georgia, on Tuesday. (AP Photo/John Bazemore)

"This is not a race about Democrat and Republican. It's not a race of right vs. left. Fundamentally, this is a race, right or wrong, and who's right for Georgia and who's clearly wrong for Georgia," Warnock told his supporters.

"This race is about competence, and it's about character. When it comes to that, the choice could not be more clear between me and Herschel Walker," he added. "Some things in life are complicated. This ain't one of them."

Warnock also accused Walker of having "no vision for our state or for our country."

Raphael Warnock

Sen. Raphael Warnock, D-Ga., speaks at a campaign event in Clarkston, Georgia, on Nov. 3, 2022. (AP Photo/Bob Andres, File)

"Think about it. We've been running now for a little while, and he has yet to tell us what he actually wants to do," Warnock said. "And he claims that he has solutions. But he says he won't share them because someone else might claim they came up with it. I'd explain that if I could."

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walker with haley at campaign event

Herschel Walker, Republican candidate for U.S. Senate, speaks at a campaign event in Hiram, Georgia, on Sunday. (Elijah Nouvelage/Getty Images)

Walker, who won a Heisman Trophy and helped steer the University of Georgia to a college football national championship four decades ago, jumped into the GOP race to face off against Warnock in the summer of last year, after months of support and encouragement to run for the Senate by former President Donald Trump, his longtime friend. It is the former football star's first run for office.

Warnock, the senior pastor at Atlanta's Ebenezer Baptist Church, where Martin Luther King Jr. used to preach, narrowly defeated Republican Sen. Kelly Loeffler in a 2021 special election and is now running to serve a full six-year term.

Fox News’ Paul Steinhauser contributed to this report.