Fifa president Sepp Blatter has said football does not have a problem with racism on the field and any incidents should be settled by a handshake.
The Football Association is probing two cases of in England.
"There is no racism [on the field], but maybe there is a word or gesture that is not correct," Blatter told CNN. "The one affected by this should say this is a game and shake hands."
The 75-year-old later said his comments had been misunderstood.
"I would like to make it very clear, I am committed to the fight against racism and any type of discrimination in football and in society," Blatter said in a statement.
"I have been personally leading this battle against racism in football, which Fifa has been fighting through campaigns such as Say No to Racism."
The Swiss added: "My comments have been misunderstood. What I wanted to express is that, as football players, during a match, you have battles with your opponents and sometimes things are done which are wrong.
"But, normally, at the end of the match, you apologise to your opponent if you had a confrontation during the match, you shake hands, and when the game is over, it is over."
In his original interview, Blatter had appeared to downplay the extent of racism in the modern game.
Asked whether he thought racism on the pitch was a problem, Blatter told CNN World Sport: "I would deny it. There is no racism.
"There is maybe one of the players towards another - he has a word or a gesture which is not the correct one.
"But the one who is affected by that, he should say: 'This is a game. We are in a game, and at the end of the game, we shake hands.' And this can happen, because we have worked so hard against racism and discrimination."
Blatter's comments , with England and Manchester United defender Rio Ferdinand tweeting: "Tell me I have just read Sepp Blatter's comments on racism in football wrong....if not then I am astonished."
Speaking to BBC Radio 5 live, former Tottenham Hotspur striker Garth Crooks was equally critical of Blatter's remarks.
"Clearly Sepp Blatter is a man who's never suffered from racism," he said. "I'm shocked and somewhat dismayed."
Piara Powar, executive director of the Football Against Racism in Europe network, also condemned Blatter's comments.
"You just don't expect the world leader of football to be coming out with comments that seem ill-thought-out, [and] insensitive," he said.
"To say that something as serious as racial abuse between players can be settled with a handshake is incorrect and not the sort of thing footballers at an amateur level, at a pro level - at any level - will want to hear from football's leader."
The remarks from the Fifa president, who has led football's world governing body since 1998 and was re-elected this year, come on the same day as Liverpool striker Luis Suarez was charged by the FA for alleged racist comments towards Manchester United's Patrice Evra.
The accusation is denied by the Uruguayan and his club say he will plead not guilty to the FA charge.
England and Chelsea captain John Terry is also facing FA and police investigations following allegations that he used a racist slur towards QPR defender Anton Ferdinand in a match at Loftus Road in October. He denies the claim.