"We would like to encourage the Iranians work with the agency, we encourage strongly for them to continue dialogue on specific suspicions," Lavrov said at a press conference in The Hague on a two-day visit to the Netherlands.
Lavrov's visit to the Netherlands comes as tensions rose between the West and Iran over Tehran's nuclear activities, which the United States and its allies fear masks a drive for atomic weapons.
The Russian minister however warned against outside interference to pressure Tehran, saying "we believe it necessary to avoid anything that might undermine cooperation between the IAEA and Iran," including sanctions.
"The important thing is that whatever is being announced and done in the nuclear area must have the full control of the IEIA," Lavrov added.
The head of Russia's army said Tuesday he expected a "decision" on Iran to be taken by Western powers this summer in response to the disputed nuclear programme.
"Iran, of course, is a sore spot. Some sort of decision on it should be taken soon. It will probably be taken closer to the summer," Chief of Staff General Nikolai Makarov was quoted as saying by the RIA Novosti news agency.
Makarov provided no further comment and it was not clear if he was referring to possible military action or future sanctions.
Russia has backed four rounds of United Nations sanctions against Iran over its nuclear programme amid growing international concern that it was pursuing military aims. But Moscow has sternly warned against using military action.
Russia last month accused Western powers of trying to "suffocate" the Iranian economy and incite popular discontent with new sanctions such as the impending oil embargo by EU states.