Duco's David Higgins said the Fury camp have claimed that Hughie has picked up an injury in training and that they have given Parker the go-ahead to fight another opponent, a state of affairs that his left Higgins "shocked".
"Do I think Hughie is injured? No, I don't. I think it's make-believe," Higgins told the New Zealand Herald.
Higgins, who described the Fury camp as "clowns", said his aim was that Parker, who arrived in Auckland from his Las Vegas base yesterday, would still fight on the scheduled date of May 6 at Auckland's Spark Arena, but that it would take some time to organise another opponent.
"We want to do the right thing by the paying public," Higgins said. "We need to show them respect and we will. We as a company need to re-group and make different arrangements and we hope to do that by tomorrow morning."
Fury's withdrawal from a fight worth $1.7 million to him should have repercussions for his career. He is undefeated at the age of 22, but few reputable fight promoters are likely to want to enter into negotiations with him or his camp.
WBO president Paco Valcarcel posted on twitter earlier today that the fight was in doubt and that he knew who was at fault.
"It seems the problem lies with Team Fury," the Puerto Rico based Valcarcel tweeted.
The Furys have refused to communicate with Duco after the Kiwi company won the purse bid and the right to hold Parker's first defence of his WBO title in New Zealand.
The latest information out of England was that they would arrive on Wednesday.
Now Parker must attempt to switch his focus entirely.
