Groups demand apology
The Fifa president remarked that gay fans "should refrain from any sexual activities" during the tournament in a country where homosexuality is illegal.
"This is not a joke, this is a matter of life and death to people," said Juriv Lavrikovs, communications director at the European branch of the International Lesbian, Gay, Bisexual, Trans and Intersex Association to the Associated Press.
"I think they should come out with a strong statement and not just wash it away. We are talking about a very basic human right that is being violated."
Herman Ouseley, chairman of Kick It Out - an organisation opposed to racism in football - added: "It was all frivolity and laughter but it's a serious business — people's existence he has ridiculed.
"We can't have that from the top of the world governing body — you've got to show leadership because you've got to influence the standards of behaviour required and then you've got to enforce it when there's a failure."
In his comments, Blatter added: "We open everything to everybody and I think there shall not be any discrimination against any human beings be it on this side or that side, be it left, right or whatever."