The Kremlin hopes the games, starting on February 7 in the city of Sochi on the Black Sea, will showcase Russia's modern face more than two decades after the Soviet Union collapsed.
Putin has identified himself closely with the $50-billion (30.42 billion pounds) event.
But Russia last year upset the West and human rights activists by banning what it called the promotion of homosexuality among minors. Calls for a mass boycott of the games have failed, but the row has clouded the build-up to the event.
Critics say the law is discriminatory and part of a rolling back of human rights and democratic freedoms under Putin, who has taken a more conservative course on social issues since returning to the presidency in mid-2012.
"There is no ban on non-traditional forms of sexual interaction between people. We have a ban on propaganda of homosexuality," Putin told a meeting with young volunteers preparing for the games.
"We ban nothing, we aren't going after anyone, we have no responsibility for such contacts."
Putin said some U.S. states had laws envisaging criminal responsibility for gay sexual intercourse.
"We have no such thing, people can feel free and at ease but please leave the children in peace," he said.
Putin did not elaborate. In a victory for gay rights activists, the U.S. Supreme Court in 2003 invalidated any remaining anti-sodomy laws that prohibited sex between adults of the same gender.
In a clear message to Moscow, U.S. President Barack Obama included three openly gay athletes in his Olympic delegation and Britain said it would sent to Sochi a minister responsible for the country's same-sex marriage laws.
Moscow has said it expects more than 6,000 athletes from 85 countries and hundreds of thousands of sports fans in Sochi.
Visibly relaxed and making jokes throughout the meeting, Putin said he would like to go to some ice hockey matches during the Games if time allows.
"Everybody in our country likes figure skating, I do too. I like cross-country skiing, biathlon, Alpine skiing. This is what I know and what I like," Putin said.
(Additional reporting by Doina Chiacu in Washington; writing by Gabriela Baczynska; editing by Andrew Roche)
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