The agency said on Friday Igor Ivanov, Security Council secretary, discussed "regulation of the situation around the Iranian nuclear programme".
The agency quoted a ministry spokesman as saying: "The telephone conversation occurred at the request of the Iranian side."
A spokesman declined to confirm the report when asked by Reuters. Tass quoted him as saying "discussion of these themes will continue".
An Iranian diplomat on Thursday said Ivanov, who acts as a Kremlin envoy for unofficial contacts on controversial issues, and Iran's chief nuclear negotiator Ali Larijani had agreed to hold talks on the proposal in a telephone conversation.
The proposal, which is backed by Washington and the European Union, involves the creation of a joint Iranian-Russian company to enrich uranium in Russia.
The plan has been put forward by Moscow in a bid to allay international concerns that Iran could manufacture highly enriched uranium on its own soil to build atomic weapons.
Iran says it only wants to enrich uranium to a low grade, suitable for use in atomic power reactors.
Iranian officials had previously said they would reject any plan which denied Iran the right to build its own uranium enrichment facilities.
But, in a sudden change of tone, a senior official said on Wednesday Tehran would "seriously and enthusiastically" study the Russian plan.