Speaking at a Democratic rally at the University of Miami, Mr Biden, who served as vice president under Barack Obama, repeated previous remarks that he would "beat the hell out of" Donald Trump if they were in high school.
Mr Biden was speaking about sexual assault during the 'It's On Us' rally on Tuesday when he turned his attention to the president and his disparaging remarks about women revealed in an "Access Hollywood" tape prior to the 2016 presidential election.
"When a guy who ended up becoming our national leader said, 'I can grab a woman anywhere and she likes it' and then says 'I made a mistake', they asked me would I like to debate this gentleman?" Mr Biden said.
"I said no, I said 'If we were in high school I would take him behind the gym and beat the hell out of him."
Back in 2016, Mr Trump apologised for the lewd comments and claimed it was "locker room banter", which did not sit well with Mr Biden.
"I've been in a lot of locker rooms my whole life, I'm a pretty damn good athlete. Any guy who talked that way was usually the fattest, ugliest SOB in the room," Mr Biden added.
Mr Biden made similar comments in 2016 when he claimed if the two were in high school together, he would "take him [Trump] behind the gym".
Mr Trump was quick to respond in 2016, claiming he would "love" Mr Biden to try and fight him and called the former vice-president "Mr Tough Guy".
Earlier this month, Mr Trump reignited the back-and-forth when he referenced Mr Biden in a speech at a charitable organisation dinner.
The US president called Mr Biden "Sleepy Joe" and claimed he could "kick his ass" in a joke-filled speech.
The rally at Miami University aimed to raise awareness and create an environment where sexual assault is unacceptable.
