Anthony Joshua says he has “identified mistakes” from his defeat to Oleksandr Usyk, while Tyson Fury has advised him to dramatically change his game-plan and "swing away" for the rematch.
Fury saw any likelihood of an undisputed heavyweight championship fight with Joshua evaporate when his rival was beaten by Usyk at the weekend.
Joshua has now said: "I've watched the fight, analysed my preparations and identified my mistakes. I've learnt my lesson.
"Don't worry about me. My spirit is strong!"
Fury had earlier advised Joshua: "There are no secrets, no rocket science, to boxing.
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"Fighters today make it technical. This is just two men punching each other for 12 rounds or less.
"Go to bed early, eat right, drink plenty of water, and get stuck in! If it's not going your way with the game-plan that you've got? Change it up!
"Give your best, give all that you can, leave it all in the ring. Don't say 'should have', 'would have', 'could have'.
"Don't think: 'If I trained harder, I could have done better'.
"My advice to Joshua is; get stuck in the best way he knows how! Put your best foot forward. Swing away, swing away!"
New IBF, WBA and WBO champion Usyk has said that Joshua has 'activated in principle' a rematch clause.
Fury will defend his WBC championship against Deontay Wilder on October 9 in Las Vegas to complete their trilogy collision.
But he refused to criticise Joshua for ceding his title reign.
"I've got no interest in slating anybody or kicking anybody while they are down," Fury said. "It's not my style.
"I like to pick on people who are doing well, who are successful, on top of their game.
"I don't like picking on people who are down, probably at their lowest point, and probably mentally unstable after a loss after a long reign.
"Joshua has to do what he's got to do. I can't say I'm interested because I've got 'the Bronze Bomber' next. Whoever's next? We'll deal with them too.
"I can't be thinking about what happened in other fights. I can only think about me."
Fury stopped Wilder comprehensively in their second fight after they battled to a draw in the first meeting.
Wilder has since claimed that his ring-walk outfit tired his legs, that Fury's gloves were illegally loaded (which the WBC disproved) and that his then-trainer Mark Breland was "disloyal".
Fury said about those claims: "It made him less of a man, less of a character. If you get beaten, shake the man's hand and move on.
"Lots of fighters have lost. Muhammad Ali and Mike Tyson lost fights. It's what they do after they lose that makes them who they are.
"When some people lose, they have to make up an excuse."
Fury warned about the third fight with Wilder: "I will go full-out attack, full inventory, from round one until it finishes.
"It will either be me or Wilder, and I can't anticipate it being myself.
"It took me six weeks [with new trainer Sugarhill Steward] to go from a slick counter-puncher to an aggressive knockout puncher.
"Wilder has 17 months since we fought to change his style. He could have got a degree from college in that time if he had worked hard enough!"
Fury's US-based promoter Bob Arum of Top Rank said: "There is no heavyweight in the world that can beat Tyson Fury now or in the near future."
"It is always a possibility because there are avid fans of both fighters," Top Rank president Todd duBoef told Sky Sports. "People are connected to both fighters.
"As long as athletes have a following, matches can always be made."
Arum added: "Obviously a lot depends on whether Joshua chooses to exercise his rematch clause, and if he does that and Fury were to beat Wilder, there are other options out there for Tyson's next fight."