England and Manchester United defender Rio Ferdinand says he is stunned by Sepp Blatter's claim that football does not have on-field problems with racism.
The Fifa president said incidents on the pitch could be settled by a handshake, although he later claimed he had been misunderstood.
"Tell me I have just read Blatter's comments wrong... if not then I am astonished," said Ferdinand on Twitter.
The 75-year-old head of world football has now responded on Twitter.
Ferdinand had messaged Blatter on the social networking site: "Your comments on racism are so condescending it's almost laughable. If fans shout racist chants but shake our hands is that OK?"
The former England captain later added: "I feel stupid for thinking that football was taking a leading role against racism - it seems it was just on mute for a while."
He then tweeted again after Fifa's website published a statement from Blatter accompanied by a photograph of him hugging Tokyo Sexwale, a South African government minister and former Robben Island prisoner.
Ferdinand said: "Fifa clear up the Blatter comments with a pic of him posing with a black man..I need the hand covering eyes symbol!!"
Blatter responded on Thursday: "The 'black man' as you call him has a name: Tokyo Sexwale. He has done tremendous work against racism and apartheid in Africa.
"We have done several joint activities to raise awareness on the struggle against racism in South Africa. Fifa has a long standing and proud record in the area of anti-discrimination which will continue."
Blatter's original comments come at a time when Chelsea captain John Terry is being investigated by the police and the Football Association over alleged racist remarks made to Ferdinand's brother, QPR defender Anton Ferdinand, in a recent game between the two sides.
Liverpool's Luis Suarez has also been charged by the FA for alleged racist comments towards Ferdinand's Manchester United team-mate Patrice Evra.
Asked whether he thought racism on the pitch was a problem in modern-day football, 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 that 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."
Professional Footballers' Association chairman and Preston defender Clarke Carlisle told BBC Radio 5 live that Blatter's comments run the risk of undermining years of work aimed at eradicating racism from the game.
"We've come through some 20 or 30 years of campaigning to bring racism to the height of awareness that it is at the moment," said Carlisle, who is also an ambassador for Kick It Out, which campaigns against discrimination in football.
"To come so far on such a sensitive topic, yet in one fell swoop he can almost give carte blanche that racism is acceptable between the hours of three and five on a Saturday afternoon."
Blackburn Rovers striker Jason Roberts felt that Blatter's comments were ill-judged.
"I'm truly shocked by his comments," said Roberts. "For him to say this in public is either very honest or very foolish.
"I am absolutely disgusted, lost for words, I cannot believe he has said something like that with all the issues that have gone on. I am absolutely fuming."
Former France and Arsenal midfielder Patrick Vieira told BBC Sport: "People have to be punished and punished hard.
"Racism is not part of our game, a part of the game I love. I strongly believe there is racism in football and we have to fight against it.
"We have to work hard to condemn racism on football," added Manchester City's current football development executive.
Several former Premier League players, including Stan Collymore, Mark Bright and Robbie Savage, have subsequently called for Blatter to resign.
Former Crystal Palace and Sheffield Wednesday striker Bright said: "To say I was staggered would be an understatement.
"This is the head of world football, whose slogan is 'For the Good of the Game'. What message does this send out after two or three decades of hard work fighting racism in football?
"He should resign his position because his views are archaic and out of touch."
Premier League chief executive Richard Scudamore said it was incorrect to suggest that racism is no longer a problem in football.
"Racism exists in the world, racism certainly still exists in football, albeit reduced," Scudamore told CNN.
"There are still issues, of course there are and we're not complacent about that, but I think it's a bit of a stretch to say it doesn't exist because it does."
The Football Association added in a statement: "The FA is committed to eradicating all forms of discrimination in football, where they exist."
Speaking to BBC Radio 5 live, former Tottenham Hotspur striker Garth Crooks said: "Clearly Sepp Blatter is a man who's never suffered from racism. I'm shocked and somewhat dismayed.
"Football has to be very careful. It's the one industry that somehow sees itself as above the law. It is not.
"Players, however glorified, are employees and have to abide by the law. Sepp is a man out of time and out of touch."
Blatter later sought to clarify his comments in a statement on Fifa's website.
"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."
Anti-racism group Kick It Out said the initial comments revealed a worrying failure of leadership from Blatter.
"Shaking hands to compensate for a racial slur is not what the game has signed up to, and trivialises the work of campaigns like Kick It Out," it said in a statement.
"But leadership is needed to make headway. And comments like this don't help in the ultimate goal of kicking racism out football and making it a discrimination-free zone."