The US president is due to have several hours of talks with his Russian counterpart Dmitry Medvedev as well as a shorter breakfast meeting with the strongman former Kremlin chief and current prime minister Putin.
Russia has been eagerly awaiting the visit as proof of a change in the US attitudes towards Moscow but observers were astonished by a pre-summit interview in which Obama said Putin still had "one foot" in the Cold War.
In an interview with The Associated Press, Obama said he believed "Putin has one foot in the old ways of doing business and one foot in the new." By contrast, Obama said he had "a very good relationship" with Medvedev.
The mass-circulation Moskovsky Komsomolets newspaper said Obama was trying to break up the hitherto tight Russian ruling "tandem" of the president and the prime minister by taking sides.
"It seems that the Americans are undertaking a head-spinningly risky game with an unpredictable outcome," it said in a front-page article.
"Washington has openly interfered in Russian political life and is stretching the ruling Kremlin tandem to breaking point. There has never been anything like this in all the zig-zags of relations between Washington and Moscow."
Putin hit back at the remark with his trademark cutting style, quipping that he was "firmly standing on both legs and always looking to the future."
Obama was more conciliatory in a television interview broadcast Saturday to the Russian-language audience, saying he wanted to forge new relations on an equal footing with Russia.
"America respects Russia, we want to build relations where we deal as equals," he told the international Russian-language news channel Vesti.
Describing Russia as a "great country with extraordinary culture and traditions," he said it "remains one of the most powerful countries in the world" and is a major guarantor of "international stability and prosperity."
Labelling Medvedev a "thoughtful, forward-looking individual" who is "doing a fine job of leading Russia into the 21st century," Obama added that Putin has been "a very strong leader for the Russian people."
Obama's remarks were translated from the dubbed Russian. There was no immediate transcript in English available from the White House.
The mass-circulation Komsomolskaya Pravda daily said up to 10,000 members of the security forces would line the route Obama's convoy takes when he travels from a Moscow airport to the city centre.
The president, his wife Michelle and two daughters are to stay in a lavish suite at the Ritz Carlton hotel with views of Red Square, it added.
Obama will be hoping for a smoother reception than on a 2005 visit to Russia when a coordination mix-up resulted in the then senator and his colleague Richard Lugar being detained for three hours at the airport in the Urals city of Perm.
Russian officials have said Medvedev and Obama will sign a deal allowing the United States to transport military supplies for operations in Afghanistan across Russian territory.
Previously, Washington has only been allowed by Moscow to transport non-lethal supplies by rail. The new deal should allow the United States to transport military supplies across Russia by air.
The two sides are also set to sign a declaration setting up the framework for the renewal of the Cold War-era Strategic Arms Reduction Treaty (START), which expires in early December.
Medvedev said in a statement Saturday he expects "concrete results" from the summit that will "open up new prospects for the development of our relations".
Ties between Russia and the United States plummeted to a post-Cold War low over Moscow's August war with Georgia but have warmed significantly under Obama with both sides vowing to press the "reset button" on relations.
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