WBA and IBF champion Joshua will put his titles on the line against WBO belt holder Parker at Cardiff’s Principality Stadium on March 31.
And the British heavyweight said he will refuse to shake Parker’s hand even after the fight because of the undefeated New Zealander’s outbursts against him.
Parker and his team have made numerous claims that he will smash Joshua’s “glass chin” when they meet in front of 80,000 fans.
“In sports you’ve got the likes of Roger Federer, Andy Murray, Lewis Hamilton, Cristiano Ronaldo, Lionel Messi, LeBron James, then you’ve got people like Joseph Parker,” said Joshua.
“He’s not a respectable type of person, he can’t control himself. But that’s just how it is. You’ve got to accept people for who they are. If that’s how he wants to plan his shot, we let him crack on.
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He claimed the video evidence proved he had a “glass chin” that Parker would smash despite the fact Joshua has only been floored once in his 20 professional fights.
That was in his blockbuster with Wladimir Klitschko when the Ukrainian dropped the Brit in the sixth round but he rose to his feet to win with an 11th-round stoppage.
Joshua responded to the press conference stunt by labelling Parker a “little kid” which Parker has vowed to make him pay for.
“Anthony Joshua is in for a huge shock,” said Parker. “A couple of months ago I heard him say ‘why should I be worried about this little kid from New Zealand’?
“Well, now he’s about to find out. And the world is about to find out whether AJ can really take a punch. My entire existence is now devoted to proving what the boxing world already knows.”
“He’ll be respectful after I whoop him. He might try to shake my hand. I won’t shake his hand though.”
Parker’s team believe they have goaded Joshua into taking the fight which will see the pair split a purse of about £25million.
They are expected to try to get under Joshua’s skin further at the official press conference this week and even plan to bring “props” in a bid to rile the British star.
They already staged a bizarre press conference in November to call out Joshua and during it Parker’s promoter David Higgins played a video clip of the Watford-born fighter’s worst moments in the ring.