The visit comes after Barack Obama, the US president, vowed on a visit to Moscow in July, to “reset” US-Russia relations.
During Tuesday’s meeting the two foreign ministers discussed new US plans for missile defence as well as their latest plans on replacing the 1991 Strategic Arms Reduction Treaty (Start).
Lavrov had called for “full clarification” about the new sea-based missile defence system which Obama 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”.
Iran says uranium enrichment is a
Start, which places strict limits on the US and Russian nuclear arsenals and is seen as a cornerstone of Cold War-era strategic arms control, expires on December 5 and negotiators have been seeking to thrash out a successor agreement.
Neave Barker, Al Jazeera’s correspondent in Moscow, said: “It’s been believed for a very long time that the bargaining tool, as it were, from the United States making a U-turn on the missile defence shield was for Russia to place more pressure on Iran.
“There is undoubtedly now more international pressure on Russia to support US action against Tehran but we’ll have to wait and see.
“Over the course of the week we’ll have a clearer idea of where Russia is likely to take it’s new ties with the US and undoubtedly Iran will be at the crux of that new era in relations.”
Also on the agenda was North Korea, which set off another round of short-range missile tests on Monday and, according to South Korean media reports, is poised to launch more missiles on Tuesday.
Nato expansion, the situation in Georgia after its conflict with Russia last year and human rights are also expected to feature in the talks.
A senior state department official said Clinton, who consulted British allies on Iran on Sunday, will ask Medvedev and Lavrov “what specific forms of pressure Russia would be prepared to join us and our other allies in if Iran fails to live up to its obligations”.
The official, speaking to reporters on the condition of anonymity, confirmed that sanctions would be discussed as a form of pressure.
The US, Russia, China, Britain, France, the five permanent members of the UN Security Council, along with Germany – the so-called P5-plus-1 group, has demanded that Iran halt its disputed uranium enrichment programme.
The West fears the programme masks a drive for a bomb – a charge Tehran denies, saying it is only for peaceful nuclear energy.
The P5-plus-1 has been instrumental in getting the UN Security Council to adopt three rounds of sanctions against Tehran, although Russia and China have resisted tougher sanctions.
Soon after Washington’s U-turn on the missile defence facilities in Poland and the Czech Republic, however, Medvedev said last month that in some situations sanctions could be “inevitable”.
The US state department official said Clinton wants to discuss a proposal in which Iran could ship uranium to Russia for enrichment there, which would ease concerns about what the uranium would be used for.
Iran on Monday dismissed Clinton’s warning that the P5-plus-1 group would not wait forever for Tehran to prove it was not developing nuclear bombs.
“The international community will not wait indefinitely for evidence that Iran is prepared to live up to its international obligations,” Clinton said in London on Sunday.
But Hassan Qashqavi, a spokesman for Iran’s foreign ministry, said “if there is a deadline or any kind of threat in their comments, they will not impact us in any way”.