Tyson Fury and Deontay Wilder had to be separated at the press conference to promote their WBC heavyweight title fight at the Staples Centre in Los Angeles on 1 December.
Fury had already dismissed suggestions he was the "challenger" to the champion, from America, before getting out of his seat and demanding Wilder join him for a "body spar".
"I am no challenger for no man. I'm the linear heavyweight champion of the world, the best of the best," Fury had said.
"This is two champions colliding, equal rights, rephrase and start again."
A similar exchange had taken place between Fury and Wladimir Klitschko before they fought in 2015, when the challenger's anger suggested he felt under intense pressure.
He later produced an impressive composed performance to secure one of the biggest shocks of the modern era in securing victory and the WBA, WBO and IBF world titles.
The Wilder bout will be just the third time Fury has fought since beating Klitschko. He tested positive for steroid nandrolone that year and cocaine in 2016, leading to the suspension of his boxing licence until earlier this year.
Before the press conference, Wilder labelled Britain's Anthony Joshua a "coward" for failing to secure a bout between the two.
Joshua was in negotiations with Wilder's team earlier this year to organise a fight which would have presented the opportunity for either man to become undisputed heavyweight champion of the world.
However, talks fell through with both sides blaming the other for the breakdown. Joshua instead fought and knocked out Russian Alexander Povetkin at Wembley Stadium last month which took him to 22 fights unbeaten.
"Hey Joshua, me and Fury have got this thing going on to see who is the biggest and baddest in the world, to see who is champion, one face, one name, something you was too coward to do," Wilder said on ITV's Good Morning Britain on Monday.
"You was a coward, and you know this, your team knows this. Every last one of you saying things over again, you manipulated it, you conjugated it. (You are) Compulsive liars."
Later on Monday, Wilder and Fury, both of whom also boast unbeaten records, had to be separated at a news conference after squaring up to each other.
Fury, 30, himself a former heavyweight champion, has fought once since returning to the ring after two and a half years following a doping ban. He beat Italian Francesco Pianeta on points in August.
