"Our repeated efforts to have Abkhazian representatives invited to an informal UN Security Council meeting have failed unfortunately over the unconstructive position of the U.S. administration, which has again denied them entry visas," Andrei Nesterenko said.
As New York is home to the United Nations headquarters, the United States is obligated, apart from in extraordinary circumstances, to allow foreign leaders to speak before the world body.
Russia proposed holding an informal UN Security Council meeting with representatives of Abkhazia and South Ossetia, the Georgian breakaway regions recognized by Moscow after a brief armed conflict with Tbilisi in August.
Russia's ambassador at the UN, Vitaly Churkin, earlier said the Council had expressed an interest in such a meeting.
Nesterenko said last month visa applications for South Ossetian and Abkhazian representatives had been submitted to the U.S. Embassy in Moscow.
It is not clear whether representatives of South Ossetia, which Georgia attacked in early August to retake it under central control, will be able to travel to the U.S.
The U.S. initially refused to issue a visa to Abkhazia's foreign minister, Sergei Shamba, in April 2007. Russia accused Washington of preventing a side in the conflict from speaking before the UN. The U.S. said Russia was trying to raise "false analogies" between Abkhazia and Kosovo complicating the discussion.
The Georgia conflict further stained relations between the U.S. and Russia. Washington accused Moscow of excessive use of force and violating Georgia's territorial integrity. Moscow said the U.S. administration had encouraged Georgian aggression.