"There are grounds to expect bright victories," Medvedev told the athletes. "We will not make predictions, but we will pull for you with all our hearts, keep our fingers crossed and believe in your victory and skills."
He gave special encouragement to the sportsmen and women making their debut at this Olympics, which begin in Beijing on August 8.
"Sports like those who dare, and luck is on newcomers' side," Medvedev said.
The Russian team is made up of 467 athletes, who will compete in 244 events.
The country's Olympic Committee said 12 billion rubles ($513.7 million) had been spent on preparations for the 2008 games.
The Russian team finished third in the medals table at the 2004 Summer Olympics in Athens.