President Vladimir Putin passed the law in June as part of a wider political crackdown but it has cast a shadow over the build-up to next year's Winter Olympics in Sochi over claims it infringes fundamental rights.
Obama said Friday he was "offended" by the law, but stressed that a boycott of the Games would be inappropriate.
Pressure on Moscow has mounted this week after the openly gay British actor Stephen Fry called for Russia to be barred from hosting the Games over what he called the "barbaric" law.
The country's sports minister Vitaly Mutko on Thursday stoked the issue further by saying athletes, activists and the international community should "calm down".
But he said on Friday that the clamour for athletes to stay away was only "light pressure", adding: "We should not be afraid of an Olympic Games boycott.
"Russia must understand that it is stronger, no matter how much someone may dislike this fact," he was quoted as saying by the Interfax news agency.
The law has however sparked anger. On Friday evening, more than 300 people took part in a "kissing party" in a show of defiance outside the Russian consulate in Antwerp, Belgium.
Obama stressed however that no one should boycott the Games.
"I want to just make very clear right now, I do not think it's appropriate to boycott the Olympics. We've got a bunch of Americans out there who are training hard. Who are doing everything they can to... Succeed," he said on Friday.
