The 30-year-old challenges Wilder for the one world heavyweight title he has never held at the Staples Centre in Los Angeles on December 1, and they had to be separated at the conclusion of an increasingly tense press conference in London.
They will also visit New York and LA to continue promoting their fight before the end of the week — following Wilder flying to Belfast for Fury’s victory over Francesco Pianeta in August — and Fury has insisted that in their more private moments together Wilder retreats into his shell.
In public both fighters consistently cut brash and confident figures, but Fury said: “He hasn’t got what he says he’s got. I see fear in Deontay Wilder, I could sense his heartbeat through his suit.
“I know when a man’s scared – Wilder’s terrified of me. He’s timid when he’s around me – looks at the floor, doesn’t make eye contact, all that sort of stuff. Even when he’s around me, off-stage.”
Fury has been accused of only taking such a dangerous fight, just the third of his comeback, for the significant purse he will be paid.
The powerful Wilder has stopped each of his previous 39 opponents, but Fury also believes that the American is wary that will not be enough.
“I don’t need any more fights,” he said, having previously revealed he would have preferred a further warm-up before December, which could define his career.
“I don’t need one more fight. If it’s going to be his easiest fight then he should knock me out in one round, shouldn’t he? With one punch.
“(Wladimir) Klitschko was a proven puncher who banged me right in the chin — it didn’t do anything. He was catching me throughout the fight with big shots — it didn’t do a thing.
“Everyone who’s a massive puncher can’t take one back, because they load up with everything, leave themselves wide open, and wallop. All of a sudden they’re looking up at the stars.
“If I say I’m ready to fight, I’m ready to fight. If I wasn’t ready, I wouldn’t take the fight.”
Fury had a similarly-aggressive exchange with Klitschko at the first press conference to promote the fight he unexpectedly won in November 2015.
It was later largely felt that he had got under the then IBF, WBA and WBO champion’s skin, but Wilder said: “Guys try to get into my head because my mind’s so strong.
“He thinks that by talking like he did with Klitschko, and getting inside his head, it’s going to be the same thing, but I’m a different person. You can’t do that with me.”
Asked about a rumoured rematch clause in his contract, in the event of a Fury victory, and if that meant a rematch could take place in the UK, he responded: “There’s a lot of things in the contract. Anything could happen — I’m going to fight over here eventually, one day, whether it’s Fury, whether it’s [Anthony] Joshua, whether it’s [Dillian] Whyte.”
:: Fury v Wilder is live and exclusive on BT Sport Box Office, December 1. For more info go to btsport.com/boxoffice