Donald Trump has threatened former vice president Joe Biden with violence, describing him as "weak, both mentally and physically".
The US President added that his Democrat rival would "go down fast and hard".
It follows comments from Mr Biden, who said he would "beat the hell" out of the President if they were in high school together and Mr Trump disrespected women.
Tweeting his response, Mr Trump wrote that "crazy" Joe Biden was "trying to act like a tough guy".
He added: "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!"
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
Mr Biden made his comments at an anti-sexual assault rally at the University of Miami on Tuesday.
The man who supported Barack Obama through two terms at the White House commented: "A guy who ended up becoming our national leader said: 'I can grab a woman anywhere and she likes it.'
"If we were in high school, I'd take him behind the gym and beat the hell out of him."
Mr Biden added that any man who disrespected women was "usually the fattest, ugliest S.O.B. in the room".
He was referring to comments Mr Trump made in a 2005 tape about groping women.
In them, the current occupant of the Oval Office said that "when you're a star", women will let you "grab them by the p****. You can do anything".
After the remarks became public in October 2016, he said he was sorry "if anyone was offended" by the "locker room banter".
Mr Biden also referred to those remarks in the month they emerged, again saying that if he and Mr Trump were in high school, he would take him "behind the gym".
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He said Mr Trump's words could be interpreted as: "'Because I'm famous, because I'm a star, because I'm a billionaire, I can do things other people can't.'
"What a disgusting assertion for anyone to make," Mr Biden said.