"Through quiet diplomacy, send the message clearly to the Chinese that this is an opportunity, with the whole world watching, to show that they take into account and want and are determined to treat their citizens with dignity and respect," National Security Adviser Stephen Hadley said on "Fox News Sunday."
Bush said he was attending the Summer Games to support U.S. athletes and to discuss human rights issues with China. Some other world leaders have said they would boycott the opening ceremonies to protest China's human rights record and its crackdown on Tibet.
Retired Olympic athlete Joey Cheek, a founder of Team Darfur, a international coalition of athletes raising awareness about the Darfur crisis, said the alliance's athletes can "use our voices" to press Darfur's case.
"Team Darfur ... can raise awareness about what's still happening in Darfur, for example, and really point out the connection between governments, and especially China, and the leverage they have over Sudan," said Cheek, who one a gold medal in speed skating in 2006.
International Olympic Committee rules ban participants from making political statements.