White House deputy press secretary Raj Shah said Thursday that President Trump Donald John TrumpBubba Wallace to be driver of Michael Jordan, Denny Hamlin NASCAR team Graham: GOP will confirm Trump's Supreme Court nominee before the election Southwest Airlines, unions call for six-month extension of government aid MORE would welcome the chance to take on Joe Biden Joe BidenJoe Biden looks to expand election battleground into Trump country Trump puts Supreme Court fight at center of Ohio rally Special counsel investigating DeVos for potential Hatch Act violation: report MORE in a campaign after the two leaders traded barbs about fighting one another.

“We’d like to see him at the ballot box. We’d like to see him in the boxing ring,” Shah said on the Hugh Hewitt Radio Show.

“You know, this president obviously can speak for himself and hold his own, but you know, I think that Joe Biden’s rhetoric has been over the top,” Shah added.

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Biden, who has been the subject of much speculation that he will run for the White House in 2020, said Tuesday that he would have “beat the hell out of" Trump in high school for comments the president has made about women.

"They asked me if I’d like to debate this gentleman, and I said 'no.' I said if we were in high school, I’d take him behind the gym and beat the hell out of him," Biden said, according to ABC News.

Trump hit back on Thursday, tweeting that if he fought Biden, the former vice president “would go down fast and hard, crying all the way.”

“Don’t threaten people Joe!” he added.

Crazy Joe Biden is trying to act like a tough guy. Actually, he is weak, both mentally and physically, and yet he threatens me, for the second time, with physical assault. He doesn’t know me, but he would go down fast and hard, crying all the way. Don’t threaten people Joe! — Donald J. Trump (@realDonaldTrump) March 22, 2018

Shah told Hewitt that Biden had his chance to take on Trump "in the ring, so to speak," by running in the 2016 election.

"He could have in the last election. He could have actually, you know, jumped in and faced him and taken on Hillary Clinton Hillary Diane Rodham ClintonJoe Biden looks to expand election battleground into Trump country Biden leads Trump by 12 points among Catholic voters: poll The Hill's Campaign Report: Biden goes on offense MORE as well and tried to challenge him," Shah said.

Biden opted not to run in 2016, and has cited the death of his son, Beau, as a main reason. He has said he is considering a 2020 campaign, but is undecided.