After Fury won an August tune-up fight, he accepted the deal to fight Wilder.
After the fight, Fury (27-0-1, 19 KOs) accused his countryman Joshua of ducking Wilder.
"You thought the first one was something?"
Deontay Wilder doesn't know how Tyson Fury got up from the 12th round knockdown. I know Deontay Wilder is going to want the rematch, but I can't speak for him. "You see many of these rich people's kids doing nothing because they had it too easy".
Fury had appeared out cold, but he returned to his feet and recovered enough to survive to the final bell.
Wilder said the bright lights of his first pay-per-view fight and a crowd of almost 18,000 fans caused nerves that led him to hunt for a knockout as opposed to staying with his game plan.
Fresh from Tyson Fury's blockbuster bout against Deontaty Wilder, promoter Frank Warren has made it clear that they are keen for a big British showdown between Fury and unified world heavyweight champion Anthony Joshua. The fight ended in a draw.
"My ultimate goal was to bring the heavyweight division back here in America", said Wilder, who won a bronze medal for his country at the 2008 Olympic Games in Beijing.
"I would love the rematch again to end the score once and for all and to ease people's mind of this worldwide controversial conversation about who really won?"
However Wilder said a rematch was all but inescapable.
"When the rematch happens, there's no excuses". I don't see why we wouldn't.
The clip, from the end of the third round, shows Fury looking up to Davison like a son to his father and asking, '"I'm boxing well, aren't I?"
"If anything, the way that fight went on Saturday works in our favour in terms of getting Wilder". I don't want no other fight to happen. "I want to give Tyson Fury the rematch ASAP".
The American will be fighting to retain the only world belt not held by Joshua, who holds three of four. "You saw the best Fury but you did not get the best Wilder and I still managed to get the job done". "They got him winning, they got me winning and some got it a draw".