In an interview with the BBC in Zurich, Blatter said he "deeply regretted" using "unfortunate words."
"When you have done something which was not totally correct, I can only say I am sorry for all those people affected by my declarations," he said. "It hurts and I am still hurting because I couldn't envisage such a reaction."
But Blatter, whose comments drew calls for his resignation in Britain and criticism from British Prime Minister David Cameron, told the BBC he does not intend to quit.
The Guardian reported Tokyo Sexwale, a black FIFA official and South African government minister, read an apology by Blatter, in which he said he is "committed to the fight against racism."
Blatter, who was re-elected to a four-year term in June, also had said racism does not exist on the soccer field, which Sexwale said "was rather unfortunate," adding, "We have had countless cases of racial slurs being spewed on the playing field by players against others."