Deontay Wilder is desperate to fight Tyson Fury after the pair squared up following the unbeaten American's successful defence of his WBC heavyweight title against Artur Szpilka.
Wilder knocked Szpilka out in the ninth round of their encounter in Brooklyn, with the Pole removed from the arena on a stretcher as a result of a knockout from a powerful right hand.
But Fury - holder of the WBA, WBO and IBO belts - entered the ring after the fight and taunted the American by chanting 'there's only one Tyson Fury'.
Responding to Fury, Wilder said: "You're just a phoney. This is just an act. You know where I am. You know what time, what place. I ain't scared of nobody. I'll come to your backyard, baby."
Fury then replied: "Any time, any place, anywhere. I'll beat you. You're a bum."
Speaking at his post-fight media conference, Wilder expressed his desire to "really hurt" Fury in a potential bout later this year, saying: "Fury's just being Fury. He's an unpredictable guy.
"I know he likes to promote, we've been trying to fight him for a while. He's just promoting, we've been doing it for four years. I feel like it's time to shut up and put up. I think it's time to get it on.
"I think it will be the biggest heavyweight fight in a long time and I will go to the UK for that one for sure. I've got my UK friends and they came to support me tonight.
"I could say a lot of things about Fury but I'm not going to spoil it. It'll be a fight that will be as big as the hype. I can't wait, I'm not playing around, 2016.
"No matter how they want to act like their big and bad, it's one thing to talk, but it's another thing when you get up in the ring. With Fury, I'm not going to have no remorse, not going to have no sympathy, I'm going to really, really want to hurt him."