The 75-year-old backtracked on remarks made in interviews earlier this week that incidents of racist abuse on the pitch should be settled by a handshake between the players concerned.
Prime Minister David Cameron led the calls for Blatter to step down, and the FIFA president admitted today that his comments had caused a “serious incident” and that he had used “unfortunate words” which he “deeply regretted”.
Blatter told BBC Sport: “When you have done something which was absolutely not totally correct, I can only say I am sorry for all those people affected by my declarations.
“I am sorry and I regret that my statements earlier this week have resulted in an unfortunate situation. I am committed to the fight against racism and I will not stop until I have stamped out racism in football.”
Blatter was adamant however, that he would not resign over the comments.
He said: “I cannot resign. Why should I?
“When you are faced with a problem you have to solve the problem. To leave the organisation this would be totally unfair and is not compatible with my fighting spirit, my character, my energy and my personal commitment to football.”
Blatter now says any players found guilty of racism on the pitch should be thrown out of the game.
“Zero tolerance,” he said.
“This was a good lesson for me as well.
It should be and it shall be zero tolerance.”
The controversy has seen Blatter become embroiled in a Twitter row with Manchester United and England defender Rio Ferdinand, and the FIFA president said he had hoped for “a little bit better more understanding from star players” because of their record in tackling racism.
Tokyo Sexwale, the South African minister who was included in a photo with Blatter when FIFA put out an initial statement on Wednesday night saying the Swiss’ comments had been misunderstood, told a press conference that Blatter had made an “unfortunate mistake” but had a long pedigree of working against racism.
He said: “We should distinguish racial remarks from other things. If you use a racial slur it won’t go away, you cannot exchange a jersey, you can’t mitigate it with a handshake, that’s why we call for action to be taken against players.
“We should differentiate between racial remarks and remarks when players are fighting for the ball.
“I think what Mr Blatter was saying, he mixed up those emotions and was trying to say ‘look, let’s get on with the game’. It was an unfortunate mistake.”
Ferdinand’s former United team-mate David Beckham joined in the condemnation of Blatter’s initial comments, calling them “appalling” and adding: “(Racism) can’t be swept under the carpet, it can’t be sorted out with a handshake.
“That’s not the way of the world and that’s not how racism should be treated.