"We expect the Iranian side to heed calls addressed to it. Then no further measures from the UN Security Council will be required," Russia's foreign ministry said in a statement.
Russia, which is building Iran's first nuclear reactor, has previously offered diplomatic support to Iran in the international crisis over the Islamic republic's nuclear programme.
But Moscow's position has shifted in recent days following Iran's delay in responding to an international package of incentives to suspend uranium enrichment that was offered by the five permanent members of the Security Council plus Germany.
On Monday, Russia voted in favour of a Security Council resolution that expressed "serious concern" about Iran's refusal to halt uranium enrichment and other work that the West suspect could help with bomb-making activities.
The resolution ordered Iran to halt nuclear activities or face the threat of sanctions, although Russian officials stressed that sanctions would not kick in automatically if Iran failed to respond.
Iranian President Mahmoud Ahmadinejad has refused to back down on the nuclear issue or to give a prompt reply to the international incentives. Iran insists it wants to enrich uranium solely to make fuel for a civilian nuclear power station.