The law has aroused concerns among activists about whether Russia is fit to host the games, the biggest sporting event it has held in its post-Soviet history.
"The law talks not about banning a non-traditional orientation but about other things, about propaganda and implicating minors," sports minister Vitaly Mutko told the R-Sport news agency.
"No one is banning a sportsman with a non-traditional sexual orientation from going to Sochi. But if he goes out onto the street and starts to make propaganda, then of course he will be brought to responsibility.
"As a sportsman, he should respect the law of a country," Mutko added. "Come (to Sochi), but don't get young people involved, don't make propaganda. This is what we are talking about," Mutko said.
Foreigners found guilty of violating the law can not only be fined up to 5,000 rubles ($156, €114) but face administrative arrest of up to 15 days and eventual deportation.
Russian officials rarely use words like "gay" and "homosexual" and prefer to use the phrase "non-traditional sexuality" to describe same-sex love.