Russia and the US have pledged to work together to ensure Iran's nuclear programme is for peaceful purposes.
After talks in Moscow with her counterpart Sergei Lavrov, US Secretary of State Hillary Clinton said Iran remained a "matter of serious concern".
She said the US was not seeking further sanctions at this stage. Mr Lavrov said Russia was "very reserved" about it.
Iran, which has recently revealed a second uranium plant, insists its nuclear programme is peaceful.
Mrs Clinton, in Moscow at the end of a European tour, praised Russia for its "extremely cooperative" work with world powers over the Iranian nuclear crisis."We believe Iran is entitled to peaceful energy but is not entitled to nuclear arms," she told reporters.
"Russia agrees with us on that."
The secretary of state added that if current talks between world powers and Iran failed, further sanctions might be inevitable - but she re-iterated that negotiation was still the preferred route at this stage.
Mr Lavrov said neither country had asked the other for anything in dealing with Iran, but "our positions coincide".
The US secretary of state is due to meet President Dmitry Medvedev at his private residence outside Moscow later.
The visit comes at a crucial moment in relations between the United States and Russia, says the BBC's Richard Galpin in Moscow.
Russia has traditionally opposed tougher sanctions on Iran but Mr Medvedev appeared to shift his stance after the revelation that Tehran had a second uranium enrichment facility in the city of Qom.
He has indicated that his government may ultimately accept further sanctions as inevitable.
No quid pro quo
President Barack Obama pledged to reset relations with Russia when he came to office and a meeting with Mr Medvedev in July went some way towards that, our correspondent says.
Since then, Mr Obama has met a key Russian demand to scrap plans to deploy interceptor missiles in Poland and a radar station in the Czech Republic as part of a US missile defence system in Europe.
Although the Americans insist they do not expect anything in return, our correspondent adds, Iran will be very high on Mrs Clinton's agenda in Moscow.
US officials say their government wants Russia to support, or at least not oppose, the idea of the UN Security Council imposing tougher sanctions on Iran if it fails to live up to its international obligations.
The council wants Iran to end uranium enrichment and has approved three rounds of sanctions - including bans on Iran's arms exports and all trade in nuclear material.
During her visit, Mrs Clinton will not meet Russia's powerful Prime Minister, Vladimir Putin. He is in China for talks focusing on trade, but also expected to raise the nuclear programmes of Iran and North Korea.
Correspondents say that if Russia and China reject new sanctions on Iran, a coalition of countries, including the EU, might take action themselves.
There are reports that this could cover stopping sales of refined oil products to Tehran.
Iran says it has a right to a nuclear programme, which it insists is designed to meet its energy needs.
The war in Afghanistan and a nuclear arms reduction treaty are also expected to feature prominently in Mrs Clinton's talks.
She has also visited Switzerland, the UK, and Ireland on her five-day European tour.