"Our relationship with Russia holds enormous potential, and we can do even more together as Russia moves along a democratic path," Rice said in a recent speech.
Rice was to arrive in Russia Tuesday for talks with President Vladimir Putin (search) and Russia's defense and foreign ministers. From there, Rice will attend a NATO (search) foreign ministers meeting in Lithuania.
Bush will join Putin in Moscow on May 9 when Russia marks the 60th anniversary of the end of World War II (search).
To Russia's annoyance, the administration has become more vocal about a perceived need for democratic reform in the country.
Bush and Putin held a somewhat awkward encounter in Slovakia in February. After Bush insisted that a country cannot be strong without democracy, Putin countered that Russia had abandoned totalitarianism (search) for good and had embraced democracy.
On that point, the administration believes that Russia has a long way to go, accusing Moscow of holding elections that fall short of international standards.
Rice said Friday she would tell Russian leaders "a democratic and vibrant and prosperous Russia is in everyone's interests."
"Our relationship with Russia holds enormous potential, and we can do even more together as Russia moves along a democratic path," she said.
The tougher U.S. line toward Russia recently may have been triggered by evidence of Russian meddling in Ukraine's election last November on behalf of the pro-Moscow candidate. Other sources of American disgruntlement with Russia include the proposed sale of 100,000 rifles to Venezuela's pro-Cuban government and perceived Russian inattention to a widespread theft of American intellectual property, including movies and computer software.
For their part, Russian leaders have long opposed U.S. policies in Iraq and worry about supposed U.S. attempts to "encircle" Russia through establishing a military presence in former Soviet republics. Washington says this concern has no basis.
Bush's May 6-10 trip will include stops in Latvia and Georgia as well as Russia.
For Rice, Russia has been a specialty for more than two decades. She served as Russia expert in the National Security Council of the first President Bush. Her visit to Moscow will enable her to practice her Russian, which is not as formidable as it once was.