Wilder responded: "We all know Fury, you are just a phony, this is just an act. You know where I am, you know what time, you know what place, I ain't scared of nobody, I'll come to your back yard."
With tension in the ring getting heated and the pair's heads getting closer, Fury said:
"Any time! Any place! Anywhere. I'll fight you in your back garden."
"Like I did Klitschko, I'll beat you, ya bum, You're a bum."
Security stepped in to separate the two fighters and Wilder hit back at Fury, saying: "You can run around like you're a preacher all you want but you step in the ring, I promise you I will baptize you.
"This is an act. You're not a real fighter. This is an act. I don't play this. You should be an actor. This ain't WWE.
"I would love to fight him next. Unfortunately I have other mandatories due. Make the date Tyson, I promise you."
Like a wrestler, Fury stood on the corner turnbuckles, gestured toward the crowd as was booed by the fans and then escorted out of the Barclays Centre by security.
A fight between Wilder and Fury may not have been signed yet - but the hype has well and truly started.
But if a fight is to happen then first Fury will have to beat Klitschko for a second time when they meet in their rematch, most likely in May, meaning any potential fight with Wilder is unlikely to happen until the second half of the year.
Before the antics in the ring between Fury and Wilder, the American struggled in his third defence of his WBC heavyweight title before producing a stunning right hand to defeat Szpilka by knockout.
Szpilka, who was bidding to become Poland's first world heavyweight champion, made it a close battle before absorbing a tough right hand to the chin with 2:24 left in the ninth round.
Szpilka (20-2) was unconscious for a few moments before recovering following the bout.
Wilder (36-0) displayed his power yet again and has now knocked out 35 opponents in 36 fights.
'He was definitely a crafty guy,' Wilder told reporters. 'I haven't competed against a southpaw in three years. He was a tough competitor, but you're fighting for a world title.
It's not supposed to be easy. I'm surprised it took that long, but we had 12 rounds and they all can't be pretty.'
- DAILY MAIL