The duo had to be separated on Monday at the first press conference in London to promote their WBC heavyweight title fight.
The pair are still to visit Los Angeles, where the fight will take place on December 1, before the week is out.
Fury told the press conference: “I want to thank everybody for turning up. And even Deontay knows to sit down in the presence of greatness.
“He can’t box, he’s knocked bums out, he fights tomato cans who can’t fight back. He’s not going to land one of those windmills on my chin.
“His a*** is going to fall out. How am I going to let this skinny little spaghetti hoop man beat me? I didn’t come here to be embarrassed by this little runt.
“To win would be a dream come true. But when I win I’m going to let him keep his belts. I don’t want that belt. I want the Tyson Fury limited edition WBC belt.
“I’m a crazy man. I want a war with this little plum. I want to break his ribs. I’m going to make this bum quit. This man has never fought a champion. And this idiot thinks he’s going to beat something.
“You all know he works for me right? He’s a dosser, carries my bags around.
“Last note, I’m going to knock this bum spark out. And you heard it here first.”
Wilder countered by telling the conference, which was streamed by US boxing broadcaster Showtime: “People want to see knockouts and I deliver that each and every time. I promise you I’m going to knock out the gypsy king. Timber!”
The pair squared up again as Fury mocked Wilder by dancing around him before both fighters were removed from the stage as the gathered crowd were singing in support of the Brit after he had earlier encouraged them to sing, “There’s only one Tyson Fury”.