Vitaly Mutko said Saturday the Universiade thus far been watched on television by 3 billion viewers in 115 countries.
By comparison, the London 2012 Olympics, believed to be the most-watched in history, drew up to 4.8 billion viewers worldwide, an International Olympic Committee representative told the trade website Inside the Games last summer.
Universiade organizers also say 3 billion people have tuned in this year - with nearly 100 million watching the opening ceremony last Saturday.
They also said 35 Russian and foreign-language broadcasters are in Kazan for the 12-day event, which runs until July 17.
ESPN, broadcasting the Universiade in North America for the first time, is carrying 115 live hours on two of its smaller channels, ESPN3 and ESPNU, which focuses on university sports.
Mutko said the sports ministry's total was arrived at "according to our data."
Viewership numbers of past Universiades were not immediately available.
"Everything is now working at the highest level," Mutko said. "The competitions are at the level of the Olympics and venues are crowded. We are very satisfied."
Whether the venues are crowded remains a matter of opinion.
The regional Tatarstan government has said more than 500,000 tickets have been sold for the Universiade's 27 events, while FISU, the officiating body for the Games, put the total at roughly 100,000.
While swimming, gymnastics and basketball have drawn throngs of spectators, organizing committee deputy general manager Igor Sivov issued a quasi-apology this week for sparse crowds at many venues, explaining that people have bought tickets but failed to show up.
Voice of Russia, R-Sport