The IOC received a letter from Russian Deputy Prime Minister Dmitry Kozak giving reassurances the host country will comply fully with the Olympic Charter's provision against discrimination of any kind.
"The Russian Federation guarantees the fulfillment of its obligations before the International Olympic Committee in its entirety," Kozak said.
However, Kozak did not back down on the issue of the new law, which penalizes anyone who distributes information aimed at persuading minors that "nontraditional" relationships are normal or attractive.
The law applies equally to everyone and "cannot be regarded as discrimination based on sexual orientation," Kozak said.
The letter still leaves open the question of what would happen to Olympic athletes or fans if they make statements or gestures that could be considered propaganda.
The law has provoked harsh international criticism ahead of the Feb. 7-23 Winter Olympics in the Russian resort of Sochi. Some activists have called for a boycott of the games, though President Barack Obama and British Prime Minister David Cameron have ruled that out.
Kozak's letter came after IOC President Jacques Rogge asked the Russians for further clarifications on the law and how it could impact on the Sochi Games.
"We have today received strong written reassurances from the Russian government that everyone will be welcome at the games in Sochi regardless of their sexual orientation," Rogge said in a statement.
The letter was addressed to Jean Claude-Killy, the French IOC member who heads the coordination commission for the Sochi Games.
It's still not clear if an athlete or spectator could be prosecuted for wearing a badge or rainbow pin or waving a small flag in solidarity with gay rights. Political gestures of any kind are also prohibited by the IOC.
The issue attracted attention at the world athletics championships in Moscow last week when Swedish high jumper Emma Green Tregaro painted her fingernails in the colors of the rainbow to support gay rights.
The gesture prompted Russian pole vault star Yelena Isinbayeva to complain that Green Tregaro was disrespecting Russia.
In his letter, Kozak said the legislation does not impose any restrictions on sexual orientation, and stressed the Russian constitution prohibits discrimination against anyone based on sex, race or religion.
The law on gay propaganda, he said, centers on the "restriction of information that promotes non-traditional sexual relationships among children."
"These legislations apply equally to all persons, irrespective of their race, religion, gender, or sexual orientation, and cannot be regarded as discrimination based on sexual orientation," he said.
The letter added: "These requirements do not attract any limitations for participants and spectators of the Olympic Winter Games in Sochi on their legal right of residence in the territory of the Russian Federation or participation in any events stipulated in the Games program that are contradictory to the Olympic Charter or universally recognized standards of international law on human rights."
Homosexuality was decriminalized in Russia in 1993 and Russian officials have been at pains to emphasize that the law does not penalize gay orientation or activity.
However, the law reflects widespread animosity toward homosexuals in Russian society and its vagueness troubles many. It appears possible that anyone wearing a rainbow flag on the street or writing about gay relationships on Facebook, for instance, could be accused of propagandizing.