In an interview posted on the newspaper's web site, Rice said that after meeting Medvedev several times, she found him "a very intelligent person. He is of another generation."
She said Medvedev has been attempting to diversify the Russian economy and work "with regions on efforts to wire the country with the Internet."
Putin's choice put Medvedev in pole position to win the March 2 presidential election. Opinion polls show some 40 percent of voters are prepared to support whomever Putin endorses.
Rice told the newspaper she hoped the election would be "really contested."
"But you know, I would hope that the time will come when Russia is going into a presidential election where there is a realistic chance for a really contested election," she said. "And I think that, to me, is the biggest problem with this."
Medvedev said Tuesday that he wanted Putin to become prime minister under him, mapping out a route for the outgoing leader to retain influence.
But Putin did not say whether he would take Medvedev up on the job offer.
U.S. President George W. Bush did not want to comment directly on Putin assuming the prime minister post, saying he does not have firsthand knowledge of Putin's plans and cautioning: "We just better let the elections play out and see what happens."
But he seemed dismissive of the idea.
"Just let me say this: It is not something I would want to do," Bush said in an interview with ABC News. "I want to serve my time as president of the country and move on and let somebody else take the helm and that is exactly what is going to happen here."
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