"Why should places go empty?" Putin was quoted as saying by R-Sport. "It's better that they're filled, and occupied by people who love sport."
Blocks of empty seats could prove embarrassing to Russian officials who hope these Games will boost their country's reputation.
Putin delivered his invitation during a visit to the mountain venues at Krasnaya Polyana. Some 25,000 volunteers are expected to help with the Games, which begin in early February.
According to news reports, higher-priced tickets for 73 medal events have yet to be sold. That includes seats for alpine skiing and the men's hockey bronze-medal game.
Luxury tickets for the opening and closing ceremonies also remained available.