President Obama put the Kremlin to the test yesterday by offering to scrap a missile defence shield in Eastern Europe if it helped to stop Iran building a nuclear bomb.

He used the second day of the Reset Summit in Moscow to urge a new era of partnership between Russia and the US in combating the spread of nuclear weapons to rogue states and terrorists.

“That is why we should be united in opposing North Korea’s efforts to become a nuclear power and preventing Iran from acquiring a nuclear weapon,” Mr Obama said.

The US plan to put a missile shield in Poland and the Czech Republic strained relations with Russia under President Bush. Moscow views the shield as a threat to its security, while Washington insists that it is to defend against a surprise attack from Iran. In a speech that was notably light on criticism of Russia, Mr Obama pressed Moscow to take more responsibility for stopping an Iranian bomb.

“I know Russia opposes the planned configuration for missile defence in Europe . . . I have made it clear that this system is directed at preventing a potential attack from Iran and has nothing to do with Russia,” he told an audience of students from the New Economic School in Moscow.

“I want us to work together on a missile defence architecture that makes us all safer. But if the threat from Iran’s nuclear and ballistic missile programmes is eliminated, the driving force for missile defence in Europe will be eliminated. That is in our mutual interest,” he said.

Russia is building Iran’s first nuclear power station and has been sceptical about American warnings about the threat posed by Tehran. It has argued against taking a tougher line with the Islamic Republic and Dimitri Medvedev, the Russian President, was the first world leader to meet President Ahmadinejad during protests against his re-election last month.

Mr Obama said that America wanted “a strong, peaceful and prosperous Russia” that would take “its rightful place as a great power” in global partnerships to deal with nuclear proliferation and violent extremism in Afghanistan and Pakistan. Moscow and Washington had learnt to respect a “balance of terror” during the Cold War but “we have to ask whether 10 or 20 or 50 nuclear-armed nations will protect their arsenals and refrain from using them.

“In 2009, a great power does not show strength by dominating or demonising other countries. The days when empires could treat sovereign states as pieces on a chess board are over,” Mr Obama added.

As he held out the prospect of a deal on missile defence, Mr Obama chided Russia for threatening pro-Western neighbours such as Georgia and Ukraine over their desire to seek membership of Nato.

He stopped short, however, of criticising Russia for recognising the breakaway regions of South Ossetia and Abkhazia after the war with Georgia in August last year.

Mr Obama said that no nation could deal with the challenges of the 21st century alone “nor dictate its terms to the world”, adding: “That is something that America now understands just as Russia understands.”

He disappointed liberal critics of the Kremlin by avoiding direct criticism of Russia over democracy and human rights. Mr Obama praised Mr Medvedev at a meeting with civil society groups for easing restrictions imposed by Vladimir Putin on non-governmental organisations.

He met Mr Putin for the first time yesterday at his country residence and praised his “extraordinary work” as President and now Prime Minister of Russia. Mr Obama had called Mr Putin a man with “one foot in the old ways of doing business” last week.

Mr Putin told Mr Obama: “We associate your name with the hopes of developing our relations.”

A senior US official later told reporters that Mr Obama had changed his view of Mr Putin and was “convinced the Prime Minister is a man of today”.

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