The 22 year-old was unhappy at what he saw as disrespect by the WBO heavyweight title holder when Parker accused Fury of being worried.
Parker initially told WBN: “I’m expecting he’s going to use the ring and run and I will have to chase him down.
“I think it’s amusing Hughie thinks I’m thinking past this fight on September 23. Hughie is gravely mistaken. I have put a massive target on Hughie’s head.
“It’s also good that he believes in himself, but during the stare down in Manchester last month, his eyes gave him away. They told a totally different story and trust me, he’s worried.”
The New Zealander also reiterated he has a one-track mind ahead of accusations he’s looking past his mandatory challenger and and assured WBN he’s solely concentrating on Fury.
“I’m not looking past September 23. My 100 percent focus is on Hughie Fury. There are no mega-fights out there unless I get past Hughie Fury,” he added.
In a direct counteraction to Parker, Hughie exclusively told World Boxing News: “I’m working harder for this than any other fight and Parker got this all wrong trust me.
“You will all see on the night what unfolds in this fight. No heavyweight can beat me, never mind Joseph Parker.”
Fury is training in an old school fashion for Parker and says his sharpening methods will show when the pair collide at Manchester Arena next month.
“You will see the matador tame the bull. I’m bred to fight and you will see what that stands for in that ring,” he said.
“Parker has one option, he has to knock me out cold to win, so let’s see if he can achieve it!
“Forget all the nice crap he said before as I heard his comments leaving New Zealand that he’s gonna chop me down to the body and knock me out. He and his team are in for a big awakening when they come here.”
In a final warning Fury added: “This time, don’t forget your belt like you did at the presser as you and your team are 1000% not going home with it.
“I come from a blood line of fighting men, not rugby players-turned boxers.
“They best make sure the camera is on that grandad (Francois) Botha when he sees what’s going to unfold as he was older than my father when Parker done him.
“Know this now, you’re in a real fight so let’s see what you got, as I’ve got all the answers for you,” said Fury.
Phil Jay is Editor of World Boxing News. Follow on Twitter @PhilDJay