Putin made the remark while meeting with volunteers at one of the Olympic venues, the Washington Post reported. A volunteer asked the president about the situation for gays in Russia.
"One can feel calm and at ease," he said. "Just leave kids alone, please."
A law adopted last year bans the promotion of "nontraditional sexual practices" to young people. While Putin and other supporters of the legislation say it is aimed at protecting children, it has effectively kept discussion of homosexuality out of newspapers and off television and has been used to ban gay pride parades.
The Russian Interior Ministry has said the law will be enforced during the games, which run from Feb. 7 to Feb. 23. It has also restricted protests to a park in a town several miles away from any of the venues.
U.S. President Barack Obama and many European leaders are staying away from the games. The delegation representing Obama includes tennis great Billie Jean King and Caitlin Cahow, a college hockey star, both open lesbians.
In his remarks, Putin said homosexual sex has not been illegal in Russia since 2003.
He suggested Obama is being hypocritical by saying several U.S. states still ban gay sex acts -- any laws still on the books were nullified by a Supreme Court ruling in 2003 -- and charged that there is a move to legalize pedophilia in some countries.