Gay people faced no discrimination at work or in society in Russia, he told BBC One's Andrew Marr Show, and the new law did not harm anybody.
"I myself know some people who are gay," he said. "We're on friendly terms. I'm not prejudiced in any way."
Gay rights campaigners have urged a boycott of the winter games.
The controversial legislation passed in June prescribes fines for anyone providing information about paedophilia and homosexuality to people under 18.
Critics say the amendment's loose wording, and its free interpretation by the authorities, effectively make any kind of public gay rights event in Russia impossible.
Some national leaders have indicated they will not attend the games, which run from 7 to 23 February.
US President Barack Obama pointedly announced he was sending an Olympic delegation that includes several openly gay sports figures, among them tennis legend Billie Jean King. (+ BBC video) » | Sunday, January 19, 2014
