Fighting a heavy cold that has dogged him throughout his European tour, President Obama had turned in early for the night to get some rest before a big set-piece speech and a third international summit in four days.

His sleep, however, was interrupted. Shortly after 4.30am yesterday he was woken in his Prague hotel by his press secretary, who told him that North Korea had fired a long-range missile.

Although the launch was neither a surprise nor entirely successful, this was the first significant security test of his presidency, and the White House was determined that the world should know that he was treating it as such.

Aides gave briefings on how Mr Obama had spent the next few hours on the telephone to Robert Gates, the Defence Secretary, as well as to other military and intelligence chiefs. “Had we determined that this launch posed a threat to the United States of America,” his spokesman said, “we would have taken whatever steps were necessary to ensure the safety and security of the American people.”

Even as he dazzles Europe, inspiring vast crowds and offering disarmament talks with Russia one day, acknowledging past US arrogance the next, the White House is acutely aware that Republicans back home say that he is an innocent abroad who promises too much for too little in return.

Yesterday, only hours before he was due to deliver a speech on his vision of ridding the world of nuclear weapons for ever, North Korea had grabbed the global spotlight and — in the eyes of critics — demonstrated that any sign of weakness from America merely encouraged its enemies.

Yesterday morning, as he addressed more than 20,000 people from Prague Castle, the President declared “America’s commitment to seek the peace and security of a world without nuclear weapons”.

The United States — as the only nation to have used an atomic bomb — had a “moral responsibility” to remove the threat of mass destruction, he said. “I’m not naive. This goal will not be reached quickly — perhaps not in my lifetime. It will take patience and persistence. But now we . . . must ignore the voices who tell us that the world cannot change. We have to insist, ‘Yes, we can’.”

At the end the crowd surged forward to touch him, as they have across Europe in the past few days. Marek Prokes, 22, a student who shook Mr Obama by the hand, said: “For me it was amazing. He is a president who can make a change. It is not just an empty phrase.” Paul Ermite, 61, declared: “That was the greatest speech I have ever heard.”

Mr Obama’s appeal to idealism, however, serves to conceal the hard-headed pragmatism of his purpose. By using a mix of exhortation and humility he hopes to overcome some of the hurdles that have for so long stood in the way of concerted international action, be it on nuclear proliferation, the economy, the war in Afghanistan or even climate change, which he later discussed at an EU-US summit.

The speech contained some important caveats, not least because much of his Czech audience is gazing anxiously at Russia’s efforts to reassert dominance over the “sphere of influence” in Eastern Europe that it once controlled with an iron fist. Mr Obama said: “Make no mistake: as long as these weapons exist, we will maintain a safe, secure and effective arsenal to deter any adversary, and guarantee that defence to our allies.”

He added that the continued threat from Iran, as well as the North Korean test launch, underlined the need for the missile shield that the US, much to the dismay of Moscow, plans to base in the Czech Republic and Poland.

Yet the main thrust of Mr Obama’s nuclear disarmament initiative shows that he is intent on building bridges with Russia, China and, to a lesser extent, European countries such as Germany, which have balked at past American efforts to stop rogue states acquiring such weapons.

Gary Samore, the President’s arms control co-ordinator, said that the US was seeking “the moral high ground” so that other countries could no longer accuse it of double standards.

Mr Obama promised that he would seek immediate ratification of the Comprehensive Nuclear Test-Ban Treaty, which the Senate has blocked previously.

In addition to the negotiations that he announced in London for a deal to cut the number of warheads held by Russia and America, he suggested yesterday that he may provide the Nuclear Non-Proliferation Treaty with the authority that it has lacked.

Mr Obama spoke of the Velvet Revolution in which the Czechs had overthrown communism without a shot being fired. He said: “It proved that moral leadership is more powerful than any weapon.”

Later he met Vaclav Havel, the playwright who inspired that movement and became his country’s first leader after the Iron Curtain fell. Mr Havel warned Mr Obama to “be careful” because he knew how idealistic hope could turn to anger. The President replied with a rueful laugh.

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