Mr Rogge said in Moscow that Russian written reassurances over the Winter Olympics in Sochi needed clarification. "We don't think it is a fundamental issue, more a translation issue."
Gay rights campaigners on Wednesday called for the games to be moved to another country in protest at the law.
The law, passed in June, prescribes heavy fines for anyone providing information about homosexuality to people under 18.
Critics say its loose interpretation effectively hinders any kind of public gay rights event in Russia.
The Sochi Games will be the biggest international sporting event in Russia since the Moscow Summer Olympics of 1980.
Sports Minister Vitaly Mutko said on Thursday that Olympic athletes would "have to respect the laws of the country" during the Games.
But, he added, Russia had a "constitution that guarantees to all citizens rights for the private life and privacy".
IOC vice-president Sir Craig Reedie has said it's highly unlikely the Games would be moved and any boycott would be damaging to athletes and to sport.