Judge Alejandro Rochin, of Mexico, scored the fight 115-111 for Wilder, Canadian judge Robert Tapper scored it 114-112 for Fury, and British judge Phil Edwards had it 113-113 to make it a draw, ESPN reported.
Saturday's bout between WBC heavyweight champion Wilder and lineal champion Fury ended in a disputed split draw at Staples Center.
Fury (27-0-1, 19 KOs), 30, of England, also has expressed interest in having a rematch, and the direct communication between Fury and Wilder is part of what helped the first fight get made.
Fury had stepped up after talks for a match between Wilder and Joshua, the WBA, WBO and IBF champion, collapsed.
Fury declared the "world knows the truth" over the result, but Wilder insists he did enough to defend his WBC title.
"Tyson and I spoke about fighting Wilder and he said, "Go and do it, make it happen".
"What? Tyson Fury doesn't bring anything to the party?"
"This rematch is the fight boxing fans want to see".
After the match, Fury said that he believed fans knew that he was the victor.
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Tyson Fury was the clear victor of his American fight with Deontay Wilder, according to Rob McCracken, Performance Director of the British boxing team and trainer to the likes of Anthony Joshua and Carl Froch. While Wilder vs. Fury lived up to the hype inside the ring, the controversial decision left many with a bad taste in their mouths.
"I wouldn't like to go through my career knowing I didn't fight the best".
"Both sides definitely, seriously want it to happen [again]", Wilder said. "We were able to see what he was able to do - get up", Wilder said. I'm a boxer, not a businessman and I'll probably go down the same route as every other boxer ... skint at the end of it all.
For much of the fight Fury frustrated the undefeated American champion with a stubbornly effective jab and deft movement, out boxing his opponent at regular intervals despite being knocked-down twice in a contest which couldn't be called.
Boxer Tyson Fury, priced at 100/1 a few weeks ago in the Sports Personality of the Year betting, is now fourth favourite to win the covetted BBC prize.
Wilder, who on Saturday had spoken enthusiastically about a possible unification fight with Joshua, meanwhile poured cold water on the idea on Tuesday.
"I got over-anxious to knock Tyson Fury out", said the 40-0-1 Wilder, who has won 39 of his fights by KO, usually with his deadly right hand. "They're getting what they deserve".
"Joshua's promoter Barry Hearn is no schmuck, he is an accountant, he has gone on the record to say they have a business plan that is all about selling tickets and making a lot of money".
But after claiming one of boxing's biggest upsets things soon turned sour and not long after the greatest night of his life he spiralled into an uncontrollable tailspin of addiction, severe depression and even suicidal thoughts with many fearing for his life let alone his boxing career. They had their opportunity but they led people on. They felt like they was the only ones that was running this sport. AJ's first choice is Wilder because when you're collecting belts, which he is, he wants to be the unified champ.