Russia's Foreign Ministry said in a statement on Saturday the Russian embassy in Tehran had given a formal note containing the offer to the Iranian authorities .
The note said that "an earlier Russian offer to Iran to establish a joint Russian-Iranian enrichment venture in Russia remains valid", the ministry said.
Iran has said that it will enrich uranium and produce nuclear fuel domestically, despite international efforts to curb its atomic programme.
Iran says its nuclear programme is directed only at producing electricity, but the United States accuses it of running a covert atomic weapons programme.
Washington is pushing for Tehran to be brought before the United Nations Security Council, where it could face economic sanctions for violating a nuclear arms control treaty.
Germany, France and Britain have suggested shifting Iran's enrichment activities to Russia, where nuclear material would be enriched only to fuel levels and not to weapons grade. But Gholamreza Aghazadeh, head of the Atomic Organisation of Iran, dismissed the offer as unacceptable earlier this month.
Russia's Foreign Ministry said its formal proposal represented a "Russian contribution into the search for mutually acceptable solutions in the context of settling the situation around the Iranian nuclear program by political and diplomatic means".