President Vladimir Putin praised the countries' positive relations, while Foreign Minister Sergei Lavrov said there was progress on key issues. But Rice also voiced careful criticism of Russia's democratic standards.
Officially, Rice was in Moscow to prepare for the visit of U.S. President George W. Bush to Moscow on 9 May to attend 60th anniversary celebrations of the end of World War II.
The talks, however, ended up touching on a range of key issues in U.S-Russian relations. After exchanging polite remarks with the secretary of state after their meeting, Putin said he and Rice had signed a series of agreements. He did not provide more detail.
"We exchanged views on a number of important bilateral and international issues and also signed several important U.S.-Russian documents. And of course we are looking forward to the U.S. president's visit [to Moscow] for the celebrations of the end of World War Two," Putin said.
Rice also expressed satisfaction at the talks and said her meeting earlier with Foreign Minister Sergei Lavrov had also been very constructive.
Briefing reporters after the meeting, Foreign Minister Sergei Lavrov said Russia and the United States had made significant progress on a series of issues, including the war on terror.
Both countries, he said, will continue their common efforts to cut financial channels for terrorist groups and eliminate weapons of mass destruction.
Lavrov told reporters that Rice and Putin also discussed the situation in Kyrgyzstan and Abkhazia, as well as their countries' cooperation with NATO and the OSCE.
Washington has been very critical of the Kremlin's moves to tighten its grip on politics and the media. Ahead of the Kremlin talks, however, Rice gave a particularly upbeat account of U.S.-Russian relations in an interview with the Ekho Moskvy radio station.
"Our presidents get along very well. The United States and the American people respect the great culture of Russia, respect the great people of Russia, and we know that Russia has a very good future ahead of it," Rice said.
"We understand that Russia is finding its own way, and we respect that. All that we are saying is that for U.S.-Russian relationships to really deepen and for Russia to gain its full potential, there needs to be democratic development." -- Rice
During the 30-minute interview, the secretary of state insisted several times that the United States was not, in her words, "an enemy." She stressed that Washington is very keen to boost cooperation with Russia in many different areas and is not opposed to Russia's interests.
She also reiterated that Russia was a strategic partner for the United States in the war on terror, the nonproliferation of weapons of mass destruction, and in solving regional issues, for instance in the Balkans and the Middle East.
However, she reasserted U.S. concerns over the Kremlin's drive to centralize power and called for greater press freedom in Russia. Washington had been very critical of Putin's move to abolish popular elections of regional governors.
"We understand that Russia is finding its own way, and we respect that. All that we are saying is that for U.S.-Russian relationships 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," Rice said.
The issue of press freedom, she said later at the Kremlin, was also raised during yesterday's talks with Lavrov.
The Russian foreign minister responded by saying that Russia welcomed discussion on any topic. But he said that the criticisms on Russia's dwindling press freedom were not specific enough to be discussed.
"We have said many times already that there are no closed topics in our dialogue either with the United States or any other partners. If they are concerned with something, we are ready to discuss specific problems and specific cases. We also noted that it is difficult to discuss simply general concerns about the alleged absence of media freedom in Russia. We need concrete examples," Lavrov said.
The divisive issue of nuclear control was also on the table.
During her interview with Ekho Moskvy, Rice praised Russia's role towards nuclear nonproliferation. The United States, she said, welcomed the recent signing of a deal between Moscow and Tehran requiring that Iran return to Russia spent nuclear fuel from its Bushehr nuclear reactor.
Rice said she had touched on nuclear nonproliferation with Russian Defense Minister Sergei Ivanov over dinner on 19 April. She said that both leaders agreed on the need to widen nuclear inspections in Russia to prevent weapons of mass destruction from falling into the hands of terrorists.
According to the secretary of state, Russia had also vowed to give the United States more access to nuclear sites.