The Gypsy King picked himself up off the canvas twice at the Staples Center, where judges scores the contest a draw, despite the Brit outboxing the Bronze Bomber.
Fury was dropped in the ninth round, as well as the 12th, where he somehow managed to rise and weather the late barrage from the America.
But many have felt the 30-year-old was robbed of one of the greatest comebacks in boxing history, with Lennox Lewis and Frank Bruno in disbelief at the score cards.
Mexican judge Alejandro Rochin somehow gave the fight 115-111 in favour of Wilder, while Canadian Robert Tapper had it 114-112 for Fury, with Brit Phil Edwards scoring the contest 113-113.
And speaking immediately after the split decision draw, Wilder said: "The rematch, I guarantee I'm going to get him.
"I would love for [the rematch] to be my next fight. Why not? Let's give the fans what they want to see.
"It was a great fight, and let's do it again. It doesn't matter to me where we do it. We're the two best in the world and we proved it tonight.
"When you get two warriors you get a great fight. That's what we proved tonight and I'm ready to do it again."
Fury echoed the statements made by Wilder, as he added: "One hundred percent we'll do the rematch.
"We are two great champions. Me and this man are the two best heavyweights on the planet."
While Fury also took the time to mock WBA, WBO and IBF champ Anthony Joshua, where he branded his compatriot as a coward.
Roaring into the mic, he said: "Where are you Joshua – you chicken?
"We are the two best heavyweights in the world right now. I am No1 and he is No2. We had the balls to put it all on the line.”
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