Sen. David Perdue won't debate Democratic candidate Jon Ossoff before the Jan. 5 Georgia runoff election despite pressure from the challenger to do so, sparking a heated back-and-forth between the campaigns less than two months before voters will head to the polls in a race that could decide control of the U.S. Senate. 

Ossoff last week challenged Perdue, R-Ga., to three debates before the runoff. The pair engaged in two debates ahead of the general election, where neither candidate reached 50% of the vote, which would have been needed to avoid a runoff. Ossoff upped the demand to six debates on Monday morning. 

"This is one of the most consequential elections in Georgia history, unfolding amid a health and economic crisis, but it appears Sen. Perdue is too much of a coward to defend his record in a public debate. If Sen. Perdue doesn’t want to answer questions, that’s fine, he just shouldn't run for reelection to the U.S. Senate,” Ossoff said in a Monday morning statement. “I offer the senator any or all of these six debates, if he has the self-confidence to debate in public.”

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"We’ve already had two debates in this election. In each, Ossoff lied repeatedly, and of course the media failed to hold him accountable," Perdue communications director John Burke said in a statement.

"He refused to talk about the issues and could not defend his radical socialist agenda. If Ossoff wants to keep lying to Georgians on TV, he will have to use his out-of-state money to pay for it," Burke continued. 

Ossoff, however, continues to insist that Perdue debate him as the senator has remained in Washington, D.C., and off the campaign trail, taking votes in the Senate. 

"David Perdue isn’t just a crook – he’s a coward, too," Ossoff said Sunday night of Perdue's decision not to participate in the debate, calling back to a line of his from a previous debate that went viral. 

The Atlanta Press Club (APC) said on Sunday that it will proceed with a scheduled debate between Perdue and Ossoff on Dec. 6 with an empty podium representing the incumbent after Perdue said that he will not participate. That promoted Ossoff to needle the senator online as "David 'empty podium' Perdue."

Georgia Public Broadcasting reported first reported the APC's podium plan. The APC told Fox News Monday that its invitation for the senator to participate in the debate still stands. A spokesperson said that "we don't feel it's fair to penalize the candidate who has agreed to come," about its plan to hold a debate with just Ossoff. 

The Ossoff campaign said Monday morning that they also accepted debates with ABC Atlanta; a joint debate with NBC Atlanta, CBS Macon and NPR Atlanta; CBS Savannah and its affiliates; ABC Augusta and its affiliates; and CNN. 

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Meanwhile, Perdue's campaign is expressing confidence that the senator will be reelected whether or not he participates in an additional debate. 

"The runoff in Georgia is an extension of the Nov. 3 general election, where 52 percent of Georgians voted against Jon Ossoff and his radical agenda," Burke said. "Perdue had a commanding first place win, outpacing Ossoff by over 85,000 votes – in nearly every other state, Perdue would have been reelected already."

Sen. Kelly Loeffler, R-Ga., and her Democratic challenger Raphael Warnock mutually canceled a debate that was scheduled between them ahead of the general election. But on Monday morning Warnock challenged Loeffler to three debates. The APC plans for one debate between those candidates to happen also on Dec. 6. It said that it is still working out details with the Loeffler campaign but it is "hopeful" that she will participate.

The previous debates between Ossoff and Perdue were highly contentious, with Perdue pushing Ossoff to answer questions on payments for documentary work that were made to him between a media company partially owned by the Chinese government while he served in his role as a CEO of a documentary company.  

“There's a responsibility there he needs to own up to, because sooner or later we need somebody in the United States Senate that will stand up to communist China,” Perdue said in a previous debate. 

Ossoff didn’t dispute the claim but said it was “so beneath the office of a U.S. senator."

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"You've continued to demean yourself throughout this campaign with your conduct. First, you were lengthening my nose in attack ads to remind everybody that I'm Jewish. Then when that didn't work, you started calling me some kind of Islamic terrorist. And then when that didn't work, you started calling me a Chinese communist," Ossoff said.

Ossoff at the debate lit into Perdue over accusations of insider trading related to the coronavirus pandemic and votes Perdue cast against the Affordable Care Act. 

"It's not just that you're a crook, senator. It's that you're attacking the health of the people that you represent," Ossoff said. His continued broadsides in the debate against Perdue went viral. 

Jon Ossoff (Left) and Sen. David Perdue (Right) are locked in a contentious runoff election for one of Georgia's two U.S. Senate seats. 

Perdue, along with a handful of other lawmakers who faced accusations of insider trading ahead of the pandemic this year, was cleared by investigations, including by the Senate Ethics Committee. 

Perdue did not appear in the final debate of the general election against Ossoff. On Perdue's refusal to participate in further debates, David Axelrod, a former senior adviser to former President Obama said: "Given the beating Perdue took in their last debate, this is no surprise."

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Ossoff and Perdue are not the only Senate candidates who will be on the ballot for Georgians on Jan. 5. Loeffler and Warnock are also in a contentious runoff for Loeffler's U.S. Senate seat after the incumbent topped Rep. Doug Collins, R-Ga., to represent the GOP in that race. 

Control of the upper chamber is essentially at stake in the January runoffs. Republicans won enough races on Election Day to control 50 Senate seats and if they win even one of the Georgia races they will have a majority in the 100-member body. 

But if Democrats sweep both Georgia races they will pull into essentially a 50-50 tie (there are two independents in the Senate who caucus with Democrats), which would allow Vice President-elect Kamala Harris to break tied votes. 

Fox News' Morgan Phillips and the Associated Press contributed to this report.