Tyson Fury's younger brother said he was "gutted" after Paul terminated their fight contract - but insisted the bout can go ahead outside of the USA.
He argued he and his team "could never have anticipated" him being refused entry to the US but Paul blasted his efforts to get a visa - claiming Fury Junior "wasn’t interested and literally went into hiding”.
Former Love Island star Fury responded in a statement: "I'm gutted and disappointed in regards to issues I have faced with entry to the USA.
"This situation has been left with my lawyers as being denied entry to a country is obviously a very serious issue and needs to be resolved.
"I am confident this fight will happen when the issues get resolved.
"I want to clarify that I will fight in a neutral country that both parties can enter.
"This can be any time, any place, anywhere."
Social media celebrity Paul had posted: "Fury’s received a termination notice. MVP did everything it could to help him & team.
"He wasn’t interested and he literally went into hiding. Second time in a row he has pulled out.
"Second time in a row I’m going to step up and take on a new opponent on short notice. AUG 6. MSG."
Former world champion Paulie Malignaggi held a mocking "moment of silence" for Fury after he was forced to pull out of the fight with Paul for the second time in eight months.
Paul, the YouTuber-turned-professional boxer, is expected to take on Hasim Rahman Jr, the son of the former heavyweight champion Hasim Rahman, on August 6 at Madison Square Garden.
Hasim's brother Sharif even tweeted it was a "done deal" - although no official confirmation has come from the two boxers themselves.
The first Paul-Fury bout was scheduled for December at Madison Square Garden, but Fury pulled out before the fight because of an infection and a broken rib.
Then Fury was not allowed to board a flight last week at Heathrow Airport in London for a scheduled news conference at Madison Square Garden.
In a now-deleted video posted to social media, Fury said that he, along with his “team” and lawyers, had “no clue” why he was denied entry.
But Tommy’s dad John had previously admitted he and other members of Tommy’s team were banned from entering the US due to Tyson’s links to mob boss Kinahan.
The ‘Gypsy King’ had already made headlines when he was refused entry into the United States as a result of the sanctions against the Kinahan Organised Crime Group.
While none of the Furys have any association with crime, the travel bans are now said to potentially jeopardise the career of both fighters.
Over 600 people, including the world heavyweight champion, are banned from entering the US at present because of their direct association with drug boss Daniel Kinahan.