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US President Barack Obama and his Russian counterpart Dmitry Medvedev are expected to announce nuclear weapons cuts when they meet later in Moscow.
Officials on both sides were quoted as saying a document had been agreed, though Russia said it was not final.
Both men say they want significant cuts - possibly down to 1,500 warheads each.
The Russian president said in an interview for Italian media released on Sunday that US missile shield plans for Europe put a "very prominent nuclear country like Russia... in a difficult situation".
A University of Maryland opinion poll released on Sunday suggests that 75% of Russians believe the US abuses its greater power and only 2% have "a lot of confidence" that Mr Obama will do the right thing in world affairs.
Neither of Russia's main TV news bulletins on Sunday evening led with the impending US visit.
"This is being played as essentially a low-key visit that shows the American leadership's respect for the Russian leadership," Dmitry Trenin, head of the Moscow Carnegie Centre think-tank, told Reuters news agency.
correspondents say Mr Obama can expect a smoother reception than he received on a 2005 visit to Russia when he and other visiting US Congressmen were detained for three hours at an airport in the Urals city of Perm.
They were kept in an "uncomfortably stuffy room adjacent to the tarmac", a US spokesman said, as they resisted Russian customs officials' demands to search their plane.
Mr Obama later brushed off the incident in his book The Audacity of Hope, saying "It wasn't the Gulag".