Obama hopes to keep building pragmatic ties with Medvedev but his introduction to Vladimir Putin, Medvedev's predecessor and current Russian prime minister, is likely to be more strained.
The US president set the stage with a pre-trip assessment that Putin still had "one foot" planted in the Cold War.
Putin, who still has a significant role in Russian politics, rejected Obama's criticism and insisted it was US policy that needed to be updated.
Obama is expected to clinch summit deals on the outlines of a new nuclear arms pact and improved co-operation in the Afghan war effort.
"On arms control issues, the negotiations on both sides are going quite progressively but there are some difficulties," Ivan Safranchuk from the Moscow State Institute of International Relations told Al Jazeera.
"There is room for some intervention from both leaders to give a boost to these negotiations."
Details of any deal remain under wraps, although the two men are expected to negotiate further cuts in the arsenals of the world's biggest nuclear powers.
The talks will form the basis for a treaty to be signed by December, when an existing pact known as START-1 expires.
The aim is to reduce the number of deployed warheads below the 1,700-2,200 allowed under the current pact.
The summit will also yield the Kremlin's permission to ship US weapons supplies across Russian territory to US-led forces in Afghanistan, sources on both sides said.
The transit deal will open up a crucial corridor for the US as it steps up its fight against the Taliban in line with Obama's new Afghanistan strategy.
But deep divisions remain over US missile defence, Nato expansion and the 2008 Russia-Georgia war.
Obama acknowledged in the Novaya Gazeta interview that there were "Russian sensitivities" over the proposed US anti-missile shield.
But he made clear he would not accept any effort by Moscow to link arms-control talks to missile defence.
Moscow, which sees proposed missile-defence sites in Poland and the Czech Republic as a threat to its security, has insisted in recent weeks that the two issues are inseparable.