He said Iran should ratify a protocol signed last year with the International Atomic Energy Agency (IAEA), and end its uranium enrichment programme.
Iran says it will reject any proposal for a complete halt to such activities.
The UK, France and Germany are to present a package aimed at convincing Tehran to give up nuclear ambitions.
The Iranian government is expected to receive the proposal next week.
The IAEA has set a deadline of the end of November for Iran to suspend all uranium enrichment-related activities.
The US accuses Iran of aiming to develop nuclear weapons, but Iran says its nuclear programme is purely for peaceful purposes.
Correspondents say Washington still favours UN sanctions against Iran but is prepared to give the Europeans a final opportunity to negotiate a settlement before next month’s deadline.
Russia is opposed to sanctions, which could threaten its $800m deal to build Iran’s Bushehr nuclear power station.
Moratorium
Mr Lavrov said there were specific steps Tehran could take to calm IAEA fears about its nuclear programme.
“The IAEA would like to see more steps promoting greater trust in the Iranian nuclear programme and Iran must take such steps,” the Russian Interfax news agency quoted him as saying.
He specified that Iran should ratify a protocol it signed last year allowing for additional IAEA inspections, and impose a moratorium on its enrichment programme.
But the Russian minister said Russia would continue to co-operate with Iran on construction at Bushehr.
Efforts to get Iran to abandon enrichment have been a failure so far, yet prospects of imposing effective sanctions on Iran through the UN Security Council are uncertain to say the least, says BBC News Online’s world affairs correspondent Paul Reynolds.
National security official Hossein Mousavian said on Saturday that Tehran would not be deprived of its legitimate right to a nuclear fuel cycle.
Mr Mousavian’s words appeared to confirm the lack of optimism that an offer to Iran would work.
However, he said Iran was ready to consider continuing its suspension of uranium enrichment and discuss new initiatives to provide guarantees that the process would never be diverted to military purposes.
Our correspondent says Britain, France and Germany feel there is a window of opportunity ahead of a meeting of the IAEA on 25 November.
The European offer is said to include a pledge to resume EU-Iran trade talks.
It is also thought to include guarantees that Iran will have access to nuclear fuel from Russia.
