Fury - who stunned Wladimir Klitschko to win the WBA, IBF and WBO belts last weekend - made outspoken comments about homosexuality in the build-up to the fight, and since then a YouTube video has emerged of the 27-year-old speaking about women and in particular Olympic champion Jessica Ennis-Hill.
The video, published on November 25, has Fury saying that Ennis “slaps up good”, while he adds: “A woman’s best place is in the kitchen and on her back - that’s my personal belief.’’
His remarks will be on the agenda when the British Boxing Board of Control meets on Wednesday.
Speaking in the ring at the Westcroft Leisure Centre in Carshalton on Saturday evening, he made an attempt to set the record straight.
“Listen, I’m the heavyweight champion of the world and people look up to me,” he said on Channel Five.
“If there’s any women in here tonight wearing dresses, I think everybody looks beautiful in a dress.
“If I am going to get in trouble for giving women compliments for wearing a dress, then what has the world come to?”
Put to him that he was the heavyweight champion of the world and his opinions carried weight, he replied: “Look, the proof is in the pudding with me. Watch this space. Don’t judge me on a couple of comments. Watch what I do.”
Fury was a controversial inclusion on the BBC’s Sports Personality of the Year shortlist earlier this week despite his comments.
The BBC has so far stood firm over his place on the 12-person list, but came under increased scrutiny after Fury’s comments on Ennis-Hill.
An online petition, set up by LGBT campaigner Scott Cuthbertson, had already collected more than 50,000 signatures demanding he is removed from the list before the latest YouTube video had been widely seen, but the network does not intend to alter the initial selections.
“The Sports Personality shortlist is compiled by a panel of industry experts and is based on an individual’s sporting achievement - it is not an endorsement of an individual’s personal beliefs either by the BBC or members of the panel,” a BBC spokesperson told Press Association Sport.
Cuthbertson believes the panel are wrong to have included Fury in the first instance and feels they would be embarrassed by reneging on their decision.
“They don’t want to go through the humiliation of taking him off the list so they are coming up with any old excuse to keep him on,” he told Press Association Sport.
“As more things are coming out, accusation after accusation about homophobia and sexism, it is making a mockery of the BBC and their flagship award.”
Fury himself tweeted to say he did not want to win the award, writing: “Hopefully I don’t win @BBCSPOTY as I’m not the best roll model in the world for the kids, give it to someone who would appreciate it.”
Heavyweight rival Anthony Joshua has told Fury he needs to conduct himself better in public.
Joshua - who has been tipped to face Fury in 2016 as he continues to make his way through the ranks - does not think Fury should change, but has told him he needs to be careful what he says and when.
He told a number of national newspapers: “You’ve got kids to grandmas listening to you so I think there’s a time and a place to say certain things. I think he has to think before he speaks. He has to be a bit more calculated in what he says. But he shouldn’t change who he is.
“He has always said outrageous things. But I think you should never change who you are - that’s important. People are going to like you or hate you.
“Sports and boxing are won on talent, not on personality. He’s become heavyweight champion of the world on talent so we have to give him credit but becoming heavyweight champion brings mad responsibility.”
Nominees for the BBC Sports Personality of the Year award are Jessica Ennis-Hill, Andy Murray, Tyson Fury, Lewis Hamilton, Chris Froome, Mo Farah, Kevin Sinfield, Adam Peaty, Lucy Bronze, Max Whitlock, Greg Rutherford, Lizzie Armitstead.