"Homosexuals athletes will be welcomed in the city, but they must "meet" the new Russian law that prohibits "propaganda of homosexuality," said Mutko.
"Nobody forbids athletes who have a non-traditional sexual orientation to come to Sochi, but they go out into the street to make propaganda, they will be held accountable before the law.
"An athlete who is in a foreign country must respect its laws." stressed Mr. Mutko. "Come (Sochi), but do not involve young people, do not make propaganda," the minister added.
In late July, the law was first applied to foreigners in Russia. Four Dutch, came a film about gay rights in Russia, have been accused of "propaganda of homosexuality".
They were each sentenced to pay a fine of 3,000 rubles (70 euros).
Russian officials rarely use the words "gay" and "homosexual", preferring to use the phrase "non-traditional sexual orientation."
Homophobia is a fertile ground in Russia, where homosexuality was considered, since the Soviet era, as a crime until 1993 and as a mental illness until 1999.