Russian President Vladimir Putin and Bush are set to meet at the three-day summit beginning Wednesday in Germany, along with the other six leaders of the G8 club of rich nations.
At a conference hosted by anti-communist activists, Bush said: "In Russia, reforms that once promised to empower citizens have been derailed, with troubling implications for democratic development."
Relations between Washington and Moscow have taken a downturn in recent months, in particular over U.S. plans to deploy its missile shield elements in Central Europe, allegedly to counter a potential threat from Iran and North Korea.
Russia has responded angrily to the U.S. plans, which include the deployment of interceptor missiles in Poland and a radar base in the Czech Republic, calling them a threat to its security. The plans, although supported by the Czech leadership, are unpopular with the Czech population.
Speaking Friday at a news conference, President Putin said the missile shield would be part of the U.S. nuclear arsenal and warned that Russia could be forced to aim its nuclear weapons at Europe.
At a separate appearance in Prague with the Czech Republic's right-wing President Vaclav Klaus, and Prime Minister Mirek Topolanek, President Bush said he would raise the issue of the missile shield at the G8 summit.
"My message will be Vladimir - I call him Vladimir - that you shouldn't fear a missile defense system. As a matter of fact, why don't you cooperate with us on a missile defense system? Why don't you participate with the United States?"
However, Putin said on Friday that Washington's cooperation proposals to Russia in the sphere of missile defense were limited to one unreasonable offer, which he dismissed as ridiculous.
"Our American partners want us to provide them with our missiles as targets, so that they can conduct exercises using our missiles," he said.
At his speech focusing on world democracy, President Bush also singled out Egypt, Saudi Arabia, Pakistan and China for their democratic records. However, he pledged to work with all partners.
"Part of a good relationship is the ability to talk openly about our disagreements. So the United States will continue to build our relationships with these countries, and we will do it without abandoning our principles or our values," he said.