"I want to reassure you that Russia will do everything in its power, like before, so that the agreement, satisfying the Iranian side, ensuring Iran's rights in the nuclear sphere is reached," Ryabkov, who is Russia's envoy to ongoing Tehran nuclear talks, told journalists.
Russia is against unilateral sanctions and pressure on Tehran, according to Ryabkov.
"And it is important that now we are close to a solution which would relieve the Iranian people, the Iranian state from this sanctions pressure," Ryabkov added.
Russia is one of the so-called P5+1 group of mediators that have until the end of June to hammer out a final nuclear deal with Iran to settle the parameters of its nuclear program in return for easing of sanctions.
The West has been pressuring Tehran over what it regards as nuclear activities aimed at creating a nuclear weapon. The Islamic republic maintains its nuclear research is for solely peaceful purposes.
On Thursday, the US Senate passed the Iran Nuclear Agreement Review Act requiring congressional review of any US nuclear deal with Iran, in a move that is feared to impede the negotiations.
But Ryabkov said Saturday that Moscow does not regard the passage of the US legislation as a threat to the Iran nuclear talks.
"I do not think there is a threat that anti-Iran or anti-Russia forces in the US Congress would resort to procedural tricks or use provisions of this legislation to torpedo the agreements," the senior Russian diplomat said.
Following the passage of the bill, US Senator Bob Menendez confirmed to Sputnik that US and Iranian negotiators will now face additional oversight. Under the bill, Congress will have 30 days after the deadline on the deal expires on June 30 to review the accord with Iran and pass a resolution of disapproval.