Hirst, whose own artworks have caused controversy in the past, made his remarks in the run-up to the anniversary of the attacks.
He told BBC News Online in a video essay: "You've got to hand it to them on some level," he said of the attackers, "because they've achieved something which nobody would have thought possible, especially to a country as big as America".
"So on one level they need congratulating, which a lot of people shy away from, which is a very dangerous thing."
However, he has now issued a statement through his company Science Ltd apologising for his remarks and saying that he is not a supporter of terrorism.
"Concerning statements I made about the atrocities committed by terrorists on 11 September I feel it is important to make my feelings clear," he said.
He continued: "As a human being and artist living in the civilised world I value human life above all else and abhor all acts of terrorism and murder.
'Wicked'
"I apologise unreservedly for any upset I have caused, particularly to the families of the victims of the events on that terrible day.
"I in no way condone terrorism of any kind and I deeply regret any offence caused by the misrepresentation of my thoughts and feelings."
In his video essay, he said the terrorist attacks were "wicked" and "devised visually".
He said: "I think the idea of looking at the 11 September attacks as an artwork is a very difficult thing to do.
"But I don't think artists look at it in a different way."
Pete Clifton, editor of BBC News Online, said: "The interview with Damien Hirst was one of a range we carried as part of our video essays to mark the 11 September anniversary.
"We are happy to make clear that Mr Hirst now wishes to apologise for some of his comments."