Fury called Joshua a "chicken" and a rematch between him and Wilder looks inevitable in the wake of their controversial draw.
Meanwhile, Fury limited Wilder to 71 connects (six per round) and Klitschko to 52 when he fought against him (four per round).
Wilder believes that he was the clear victor of the bout.
"To beat the champion you must dominate the champ and to me I was the more aggressive fighter and landed the more effective punches".
Fury claimed Joshua would have been "nailed" by Wilder, and said his domestic rival has "my belts" - a reference to the titles he held after defeating Wladimir Klitschko in 2015 before relinquishing them due to inactivity.
Joshua will next fight at Wembley Stadium on April 13. Fury got up quickly and rallied to almost winning back the round as Wilder appeared as if he might've punched himself out going for the finish.
Tyson Fury left and trainer Ben Davison have enjoyed a fine relationship
"I am going out to LA and we will talk (with Wilder's representatives) this week". You can't take anything away from me or Wilder and you can't let the decision take away from how good a fight it was. It's time to dissect the fallout of the massive fight in the Deontay Wilder vs. Tyson Fury post-fight press conference.
The previously-unproven Davison, 26, had been considered a potential weakness in Fury's preparations but in only their third bout together he oversaw a performance that suggests the fighter is again the world's finest heavyweight.
Frank Warren plans to begin negotiations for a lucrative rematch between Tyson Fury and Deontay Wilder imminently.
"If it was up to me - and only me - I would like to do the Fury fight first because I think there is unfinished business. Both the guys put on a tremendous fight", Deas told the BBC. That has always been the fight we want because he has the last belt.
However, rather than the rematch the boxing world would undoubtedly love to see, Wilder's team have indicated they have a heavyweight unification bout with Anthony Joshua in their sights.
RBI keeps interest rates unchanged
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