Prior to Tuesday's talks, a senior US official had said that Clinton wanted to know "what specific forms of pressure Russia would be prepared for to join us" if Iran did not keep promises not to pursue nuclear weapons.
But Lavrov said that Russia's long-standing position that any talk of sanctions against Iran at this stage was counter-productive.
At a joint news conference in the Russian capital, Clinton said they had held "productive and comprehensive discussions."
But she did not succeed in getting any detailed pledges from Moscow on sanctions.
'Not at that point'
Clinton said she agreed with a recent statement by Dmitry Medvedev, the Russian president, that sanctions against Tehran may be inevitable if no progress was made, but said "we are not at that point yet".
"That is not a conclusion we have reached. And we want to be very clear that it is our preference that Iran works with the international community ... to fulfil its obligation on inspections," she said.
Clinton's visit to Moscow is her first since becoming Washington's top diplomat and comes a week before international talks on a proposal to send Iranian uranium abroad for further processing.
Nazanine Moshiri, Al Jazeera's correspondent in Tehran, said it was "extremely important" for Iranians not to have the immediate worry of sanctions.
"They don't want a forfeit round of sanctions right now. That's why they're keen to continue this diplomatic track and keen to talk to the Americans at Vienna on October 19th," she said.
"And also to open up [the nuclear site of] Qom to inspections. It's a very clever move by the Iranians to continue this track."
On negotiations aimed at replacing a key Cold War-era nuclear disarmament treaty by the end of the year, Lavrov said there had been a "substantial movement forward".
The 1991 Strategic Arms Reduction Treaty (Start), which places strict limits on the US and Russian nuclear arsenals, expires on December 5 and negotiators have been seeking to thrash out a successor agreement.
Lavrov also said Russia and the US should work more closely on missile defence plans, after Washington's recent shelving of a missile defence system in Eastern Europe ended a major dispute with Moscow.
The Russian foreign minister had called for "full clarification" about the new sea-based missile defence system which Barack Obama, the US president, unveiled last month to replace an earlier version, backed by his predecessor, George Bush, to deploy missile defence facilities in Poland and the Czech Republic.
Russia had fiercely opposed Bush's plan and welcomed Obama's move to alter it as a "responsible approach".
Lavrov confirmed that he and Clinton had also discussed the Middle East, North Korea and Afghanistan.