It's much easier to explain why Russian President Vladimir Putin wants a multilateral deal with Iran than U.S. President Barack Obama. The political and economic gains from the removal of United Nations-imposed sanctions are palpable for Russia, while iffy at best for the United States.
Putin's moves since a framework deal on Iran's nuclear program was agreed upon on April 2 indicate how he plans to develop Russia's partnership with Iran. One is arms sales, as indicated by the recent decision to permit the stalled shipment of S-300 anti-aircraft missiles, and the other is oil deals, as exemplified by a purported oil-for-goods swap.
Neither decision required the lifting of sanctions against Iran — these were voluntary restrictions Putin could have ended even without the prospect of a multilateral deal. He's trying to get a foot in the door first, before his Western adversaries start making inroads into the Iranian market, and focusing on areas where Russia is competitive. The potential gains are significant.