As Democrats and some Republicans tried to quash claims that non-citizen voting had an impact on November's election, others embraced the opportunity to reignite the debate.

President Donald Trump told congressional leaders Monday that "illegals" had cost him the popular vote, reigniting a quarrel over a claim that has been largely dismissed by independent fact-checkers.

"It is a shame when people get elected to office and they use their ideas and their voice with absolutely no facts and they do things as ridiculous as infringing upon the confidence of our democracy," Rep. Tony Cardenas (D-Calif.) told The Hill Tuesday.

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Some top Republicans were just as quick to dismiss the allegations of voter fraud.

Speaker Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (R-Wis.) reiterated that he's seen "no evidence to that effect," and Sen. Lindsey Graham Lindsey Olin GrahamThe Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Senate Democrats' campaign arm announces seven-figure investment to boost Graham challenger Graham: Comey to testify about FBI's Russia probe, Mueller declined invitation MORE (R-S.C.) asked Trump to show proof of the claims "or please stop saying it."

But some House Republicans used the president's claim to revive their own accusations of widespread voter fraud.

Rep. Steve King (R-Iowa) was asked on MSNBC Tuesday whether he believed Trump's accusation that 3 million to 5 million people had voted illegally. King said he wasn't aware of that figure, but said he had extrapolated a figure based off a study of voter fraud in two Virginia counties.

"The number I came up with off of that extrapolation was 2.4 million," said King. "So it's plausible -- the number 3 million sounds like it's a plausible number to me."

House Democrats railed against King, who has been a hardline proponent of restrictive immigration measures.

King blamed alleged illegal voting partly on simplified voter registration techniques, such as registration connected to driver's license applications.

"They ask them if they want to sign up for under motor voter, register to vote. Maybe they don't understand the language, maybe they understand," King said. "They can be signed up anyway. But some of them go in and vote. I'm completely convinced of that. I don't know the number. We need to clean it up. And motor voter is a gateway to illegal voting."

"That's provably incorrect. But then, that's Steve," said Rep. Zoe Lofgren (D-Calif.) of his figure estimate.

"Steve King is a paranoid politician that is trying to basically be divisive and disempower all people of color that vote. The fact is that the instances of voter fraud are rare, the incidence among immigrants is rare, and the incidence of undocumented immigrants voting is almost nonexistent," said Rep. Ruben Gallego (D-Ariz.).

Rep. Mo Brooks Morris (Mo) Jackson BrooksOvernight Defense: Trump hosts Israel, UAE, Bahrain for historic signing l Air Force reveals it secretly built and flew new fighter jet l Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' OVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals,' official says MORE (R-Ala.) said it was impossible to determine how many non-citizens had voted in the past, but said measures should be taken going forward to ensure voters proved their citizenship in the registration and voting process.

"There's no proof of substance one way or the other, but there are enough circumstances to cause people to have different opinions on this issue," said Brooks.

He cited the elections of Sens. Al Franken Alan (Al) Stuart FrankenPeterson faces fight of his career in deep-red Minnesota district Getting tight — the psychology of cancel culture Tina Smith wins Democratic Senate primary in Minnesota MORE (D-Minn) in 2008 and Maria Cantwell Maria Elaine CantwellHillicon Valley: Zuckerberg acknowledges failure to take down Kenosha military group despite warnings | Election officials push back against concerns over mail-in voting, drop boxes Bipartisan senators call for investigation of popular fertility app The Hill's Coronavirus Report: Mike Roman says 3M on track to deliver 2 billion respirators globally and 1 billion in US by end of year; US, Pfizer agree to 100M doses of COVID-19 vaccine that will be free to Americans MORE (D-Wash.) in 2000 as examples of elections that could have been decided by ineligible voters. Franken beat then-Sen Norm Coleman (R-Minn.) by 312 votes, and Cantwell beat then-Sen. Slade Gorton (R-Wash.) by 2,229 votes.

"That's an example of where illegal votes could have swayed the outcome, and there are any number of House seats that are decided by less than one percentage point," said Brooks.

Sen. Bernie Sanders Bernie SandersMcConnell accuses Democrats of sowing division by 'downplaying progress' on election security The Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Why Democrats must confront extreme left wing incitement to violence MORE (I-Vt.) also joined the fray, calling Trump's accusation "delusional" and said "he is sending a message to every Republican governor in this country to go forward with voter suppression."

California Secretary of State Alex Padilla, a Democrat who has made voter enfranchisement his signature issue, panned Trump for bringing up the claim again.

"By repeating false and unsubstantiated voter fraud allegations as the cause for losing the popular vote, President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE is dangerously attacking the legitimacy of free and fair elections and the foundation of our democracy. These are not 'alternative facts.' They are corrosive lies without any evidence. Even leaders in the President's own party agree there is no evidence to support his claims since they were irresponsibly made back in November," Padilla told The Hill in an email.