This is more than two-thirds of their original entry list of 389 athletes, despite the World Anti-Doping Agency (Wada) recommending a blanket ban after a state-sponsored doping scandal.
Russia’s Olympic Committee president Alexander Zhukov said his country will have “the cleanest team” at the Games.
The Olympics opening ceremony takes place on Friday.
“The Russian team may have experienced the toughest checks of the Olympics, because they had to go through multiple tests and checked,” said Zhukov.
“On top of all that, Russian athletes are going through additional testing which is taking place at the Olympic Village.
“So, as of now, the Russian team is probably the cleanest in Rio.”
Zhukov said it was a “flagrant injustice” that some Russian athletes would not be in Rio.
He said: “Athletes such as Yelena Isinbayeva and Sergey Shubenkov who have never been associated with the issue of doping and who are absolutely clean cannot take part in the Olympics Games, but many sportsmen like, for example, the American runner Justin Gatlin, who have served doping bans, will.”
Isinbayeva won Olympic gold in the women’s pole vault at London 2012 while Shubenkov is the world 110m hurdles champion.