Sepp Blatter said that he is sorry for causing offence with his controversial comments on racism.
The FIFA president appeared to suggest on Wednesday that racial favoritism could be settled with a handshake.
"It hurts and I am still hurting because I couldn't imagine such a reaction," said the 75-year-old Sepp Blatter .
"When you have done something which was not totally correct, I can only say I am sorry for all those people affected by my statements," he added.
Blatter persisted his "fight against racism and discrimination will go on" and said he would not resign, despite calls for him to resign by numerous British players, managers, administrators and politicians.
"When you are faced with a problem you have to face the problem. To leave would be totally unfair and not compatible with my fighting spirit, my character, and my energy."
Blatter confessed his comments had caused a "serious incident" and that he had used "unfortunate words" which he "deeply regretted".
He also added any players found guilty of racism on the pitch should be thrown out of the game.
Blatter's comments about racism, made earlier in the week, caused anxiety in England.
Manchester United defender and former England captain Rio Ferdinand accused the FIFA president of "ignorance", while David Beckham described Blatter's remarks as "dreadful".
Beckham added: "I don't think the comments were very good for this game. (Racism) can't be swept under the carpet and it can't be sorted out with just a handshake."
Former England defender Sol Campbell was not fully satisfied with Blatter's apology though.
"For me, it doesn't wash," he said. "For the head of FIFA to come out with something like that is shocking. I am surprised he's still in a job. I think he should do the honorable thing and quit.
"When racist comments come from another player, it's even more hurtful. It's terrible, it's disgusting. People saying it's ok, it's unbelievable.
"He is the head. He should know better. The longer he stays, FIFA will become weaker."
Chelsea manager Andre Villas-Boas believes Blatter's sorry should be the end of the issue.
"To put in doubt the leadership of Sepp Blatter as FIFA president is not for me to say or managers to say," he said.
"There are things that should have been avoided in the first place. But at least there is humility," he added.
