"In the interests of normalising the situation surrounding Iran's nuclear programme, Tehran should continue active cooperation with the IAEA," a Russian foreign ministry statement said.
"The voluntary adoption by Iran of the conditions in the document... would be an extremely important measure of trust, the rejection of which would not help regulate the Iranian nuclear problem in the context of the IAEA," the statement read.
Iran's conservative-controlled parliament took steps last week towards adopting a bill that would oblige the Iranian government to reject the conditions of an additional protocol to the nuclear Non-Proliferation Treaty (NPT) that allows inspections.
Iran signed the protocol in 2003 but has not ratified it and has threatened to resume uranium enrichment for what it insists is a peaceful nuclear energy programme.
Tehran froze its enrichment programme two years ago as a "confidence building measure" amid talks with the European Union on guaranteeing the safety of its nuclear program.
Russia abstained from voting on an IAEA resolution last month that found Tehran in "non-compliance" with nuclear proliferation safeguards and urged Iran to suspend activities related to uranium enrichment.
The resolution is seen as a first step towards hauling Tehran before the UN Security Council.
Russia is an ally of Iran and has an 800-million-dollar (669-million-euro) contract to build Iran's first nuclear reactor.