Rice, on her first visit to Moscow as Washington's top diplomat, on Wednesday also said the United States would be watching the outcome of oil magnate Mikhail Khodorkovsky's trial "to see what (it) says about the rule of law in Russia".
A Moscow court is to hand down a verdict in Khodorkovsky's fraud trial on 27 April.
Rice's remarks, which included accusations that Russia had no independent television channels, were unlikely to reach most Russians because all leading TV networks failed to report them.
TV kept reports of her visit brief and relegated them to a low position on news programmes, though newspapers and radio stations that enjoy greater independence gave her more coverage.
Leading Russian TV networks did
not report Rice's critical remarks
Speaking in a live interview with Moskvy radio before meeting Putin, Rice renewed charges that Russia had some distance to go in developing its democracy, including allowing the growth of an independent media free from Kremlin pressure.
Though she couched her criticism in diplomatic tones, she singled out the powers that Putin had accumulated since taking over in the Kremlin in 2000.
"All that we are saying is that for the US-Russia relationship to really deepen and for Russia to gain its full potential, there needs to be democratic development."
"There should not be so much concentration of power just in the presidency, there needs to be an independent media ... so that the Russian people can debate and decide together the democratic future of Russia," she said in reply to questions from the public sent in to the radio station via the internet.
Putin and Rice exchanged formal pleasantries before holding talks in the Kremlin and, publicly at least, there were no signs of tension between them.
"We are interested in a strong and democratic United States that performs responsibly on the world stage"
Russian Foreign Minister
Russia is considered a test case of President George Bush's vow to make democracy crucial to all Washington's bilateral relations.
Washington's support for popular revolutions that have brought pro-Western governments to power in ex-Soviet Georgia and Ukraine have alarmed Russia, and Foreign Minister Sergei Lavrov made clear Moscow wanted some kind of rules of the game to be set.
"As much as the US is interested in a strong and democratic Russia, we are interested in a strong and democratic US that performs responsibly on the world stage," he told a joint news briefing after talks with Rice.