The brash rivals began their press tour ahead of the December 1 bout in Los Angeles at the BT Sport studios in London on Monday afternoon, and will also visit NY and LA before the end of the week.
But the colourful language that has been a feature of his career was in evidence as he tried to goad Wilder, who has won 39 of his 40 fights by way of knockout.
IBF, WBA and WBO world champion Joshua - who avoids the kind of trash talk that fuels Fury - defended his titles with a brutal seventh-round stoppage of Alexander Povetkin at London's Wembley Stadium last month.
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"I am savoring nothing, the only thing I am savoring is smashing Wilder's teeth in", Fury told the news conference. I will stand and prove what I will do to this idiot. "I want to feel the punching power".
A similar exchange had taken place between Fury and Wladimir Klitschko before they fought in 2015. "Two fights, 10 fights - it doesn't really matter". If we fought 30 times, I would win 30 times. I've been out for a year, now I'm coming to you, to beat you.
UK Heavyweight boxing champ Anthony Joshua came out and said it outright: a fight with American Heavyweight Deontay Wilder is the fight he wants, "and the fight that should happen". If you can fight, you can fight. "People feel the intensity, it's a huge fight".
Fury welcomed WBC champion Wilder to London in the first stop of their world tour, which will also see the pair appear in NY and Los Angeles, the location of the fight.