In attempting to explain reasons for not being able to completely knock out Fury or win the bout on points, Wilder told reporters in LA that he had actually fractured his arm in the lead-up to the fight.
Wilder had lobbied for a fight with Anthony Joshua, who holds the other three championship belts.
"I was sparring, just getting ready and I was getting the best of my sparring partner", Wilder explained.
"My main goal is Tyson Fury".
Hopefully the rematch can be made as soon as possible.
"I don't see why not, let's do it again while it's hot and give the fans what they want to see".
"I'm ready whenever he's ready", Wilder said.
The WBC heavyweight title fight between Deontay Wilder and Tyson Fury was scored a draw which hardly anyone of note has agreed with so far in the boxing world.
"I saw his eyes roll slowly in the back of his head", Wilder said.
Fury, who only returned to boxing this year after almost three years out of the ring as he struggled with depression, drink and drug problems, had said Monday he doubted Wilder would grant him a return. "I feel like God got this man up [from the canvas] for the rematch".
However Wilder said a rematch was all but inescapable. I don't see why we wouldn't.
"Both sides definitely, seriously want it to happen [again]", Wilder said. I take nothing away from this fight but we won this fight; to beat the champion you must dominate the champion. "It's only right for us to go back in and do it again", Wilder said. I don't want no other fight to happen. "I wanted to end it on a devastating knockout and I pressed that".
Wilder, who on Saturday had spoken enthusiastically about a possible unification fight with Joshua, meanwhile poured cold water on the idea on Tuesday. "They got him winning, they got me winning and some got it a draw".
Joshua is keen to fight both Wilder and Fury. Many people felt it should have been waved off. "We don't care about him no more".
"They had their opportunity but they led people on". Their ego got the best of them. "My kids have to make their own living and make their own way in life; they won't be living off my name or reputation because that's too easy a route", he continued. Who won the first fight? I don't know how this man got up.
"When you coming in here fighting the champion, you've got to be dominant. I think the fans deserve the rematch". I was the aggressor and I thought I won.
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