Wilder's camp maintain they offered $50 million to Joshua to accept a fight, a gambit dismissed by the British boxer's manager Eddie Hearn as a "wonderful PR move".
Wilder (40-0-1, 39 KOs), 33, of Tuscaloosa, Alabama, considered by many the most devastating puncher in boxing, hit Fury cleanly with a right hand on the chin and followed with a left hook to score a brutal knockdown in the final round.
"I'm ready whenever he's ready", Wilder said. 'My main goal is Tyson Fury.
Fury claimed Joshua would have been "nailed" by Wilder, and said his domestic rival has "my belts" - a reference to the titles he held after defeating Wladimir Klitschko in 2015 before relinquishing them due to inactivity.
"I'm ready to do it again", Wilder told reporters on a conference call.
In the end, one judge scored the fight 115-111 for Wilder, one judge had it 114-112 for Fury and one had it 113-113 as Wilder retained his belt for the eighth time and Fury retained the lineal championship in his first defense.
"There are so many opinions, so many mixed emotions surrounding the first fight", Wilder said. "It's only right for us to go back in and do it again".
"I seen this guy's eyes roll slowly in the back of his head".
"They felt they were the only people in heavyweight boxing that people cared about".
"It might also be the case that Wilder fancies his chances in a punch-out with AJ rather than another go at Fury".
It now remains to be seen what direction Wilder goes in, with a rematch against Fury and the victor facing Joshua later in 2019 one possibility. "I was working from very young, everything I wanted in life I had to work for". But they led people on.
"Let them continue to fight the second-tier fighters and hopefully one knocks him out".
"Everyone wants to know what's going to happen in the second fight", Wilder continued. You've got to take the title, and I don't think Fury took the title. "I want American boxing to win".
A stark contrast from 2015 after beating Wladimir Klitschko, Fury of 2018 really seems to have finally won over the public. We are here to put entertaining fights on while we are in the era and active. Their ego got the best of them.