Fifa president Sepp Blatter insists he has fought racism "all my life" as a growing number of sporting figures call for him to resign.
On Wednesday the 75-year-old said racist incidents in football matches could be settled with a handshake at the end of the game.
In a follow-up interview on Thursday he reiterated his views, describing some comments as simply being "foul language".
"I'm not saying about discrimination, but it's foul language, it's a foul play. At the end of the match, if you have foul play [when] the match is over you shake hands now because it's what we want to do.
"Before the match and at the end of the match everyone shall shake hands and therefore also forget what has been on the field of play.
"I can tell you in all my life in football now has been accompanied by fighting discrimination and fighting racism."
Many high-profile figures in sport and politics have rounded on Mr Blatter after he made his original remarks.
Prime Minister David Cameron said: "It's appalling to suggest that racism in any way should be accepted as part of the game.
"A lot of work has gone into ridding racism from all aspects of our society, including football. As many of our top sports stars have rightly pointed out, now is not the time for complacency."
Labour leader Ed Miliband said: "I think Sepp Blatter's comments are a disgrace and I think that football needs new leadership."
Gordon Taylor, head of the Professional Footballers' Association, told Sky News the comments were "disgraceful".
"He has presided over a lot of issues that just haven't been good enough," he said. "If he's going to be the leader of world football then I'm not going to be a follower.
"I believe you can be kicked about, of course you have banter, but when that becomes racist, when that is prefaced with the colour of your skin, it is not acceptable."
Les Ferdinand - the older cousin of footballing brothers Anton and Rio - told Sky Sports News it was "about time we stopped hearing from him (Blatter)".
Asked if he believed the head of world football should now go, he said: "I certainly do.
"Like a lot of these people, they don't understand racism. It's never happened to them so they're making comments on a subject they know nothing about."
In two interviews, Mr Blatter appeared to make light of racial abuse between players during matches.
"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 also the one who is affected by that, he should say that this is a game," he said.
"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."
He later issued a statement on Fifa's website claiming he had been "misunderstood".
Mr Blatter said: "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.
"Having said that, I want to stress again that I do not want to diminish the dimension of the problem of racism in society and in sport.
"I am committed to fighting this plague and kicking it out of football."
The comments came as the FA charged Liverpool player Luis Suarez with racially abusing Manchester United's Patrice Evra .
The FA is also investigating claims that England captain John Terry racially abused QPR player Anton Ferdinand. Terry denies the allegation .
Anton's brother, Manchester United defender Rio Ferdinand described Mr Blatter's comments as "condescending" in remarks posted on Twitter.
He tweeted: "If fans shout racist chants but shake our hands is that OK?
"I feel stupid for thinking that football was taking a leading role against racism.....it seems it was just on mute for a while."
The England player was also critical of Fifa's attempts to clarify Mr Blatter's comments with a statement on their website underneath a picture of the Fifa president with South African minister Tokyo Sexwale.
Mr Ferdinand wrote: "Fifa clear up the blatter comments with a pic of him posing with a black man...I need the hand covering eyes symbol!!"
The Fifa boss replied directly to the footballer saying: "The 'black man' as you call him has a name: Tokyo Sexwale. He has done tremendous work against racism and apartheid in Africa."
The remarks have received widespread condemnation in the British media but little attention in newspapers elsewhere in Europe.
The FA-backed anti-racism group Kick It Out was scathing about Mr Blatter's remarks, accusing the Fifa president of being "worryingly out of touch".
It said: "Shaking hands doesn't resonate with the zero-tolerance approach we encourage and certainly wouldn't resonate with the victim of the abuse."
Mr Blatter recently won a fourth term as Fifa president, despite allegations of corruption among delegates.
Times sports writer Matthew Syed told Sky News: "It's an astonishing intervention from Blatter.
"He has a track record of coming out with very ill-judged comments, we've seen it before with women's clothing in football, gay rights in Qatar.
"And this is a really characteristic gaffe by somebody who many people who support football around the world cannot understand is in the position that he is."
Ladbrokes have now slashed the odds of Mr Blatter being out of his current job by the New Year to 2/1.