Mr Obama said that as long as Iran continued to pose a potential nuclear threat, the US would continue to work on a controversial missile defence shield, parts of which would be stationed in Poland and the Czech Republic.
Obama is a seducer, in the nicest possible way of course. He smiles and refers to himself as Hussein and does all the other things that make Europeans swoon
He was speaking ahead of a meeting with EU leaders in the Czech capital, Prague, hours after North Korea launched a rocket despite international warnings.
Mr Obama condemned the launch: "Now is the time for a strong international response," he said.
"North Korea must know that the path to security and respect will never come through threats and illegal weapons."
Extermination of cities
Speaking to a 20,000-strong crowd in front of Prague's historic castle, Mr Obama said the US had a moral responsibility to act in ridding the world of nuclear weapons.
As long as the threat from Iran exists, we will go forward with a missile defence system
"The existence of thousands of nuclear weapons is the most dangerous legacy of the Cold War," he said.
"Today the Cold War has disappeared but thousands of those weapons have not."
He pledged to reduce the US nuclear stockpile, and urged others to do the same.
But as long as a nuclear threat existed, the US would retain its nuclear capability, although it would work to reduce its arsenal.
He said his administration would work to bring the Comprehensive Test Ban Treaty (CTBT) into force in order to achieve a global ban on nuclear testing.
The agreement would ban all nuclear explosions for any purpose, but cannot currently come into effect as nuclear powers such as the US and China have not ratified it, and India and Pakistan have not signed it.
Massive destruction
The most immediate and extreme threat to global security, the president said, was the possibility of terrorists possessing nuclear weapons.
"One terrorist with a nuclear weapon could unleash massive destruction," he said.
OBAMA'S TRANSATLANTIC VISIT
2 April: G20 summit in London
3 April: Obama meets Sarkozy in France and Merkel in Germany
"Al-Qaeda has said it seeks a bomb. And that it would have no problem in using it. And we know that there is unsecured nuclear material across the globe."
Mr Obama announced a new effort to secure sensitive nuclear material within four years and break down the black market in the trade in illicit weapons.
He also said he would negotiate a new strategic arms reduction treaty with Russia by the end of this year.
The speech came days after he and Russian President Dmitry Medvedev - meeting on the sidelines of the G20 summit in London - agreed to reopen negotiations about reducing nuclear warheads.
They aim to produce a new arms control treaty to replace the Strategic Arms Reduction Treaty (Start) that expires at the end of the year.
Under Mr Obama's predecessor, George W Bush, tensions arose between the two sides over the US plan for a missile defence shield, parts of which would be stationed in Poland and the Czech Republic.
The new US administration is currently reviewing the plans, which are meant to counter nuclear attacks from countries like Iran and North Korea, but which Moscow sees as a threat.
Mr Obama said his administration would also seek to engage with Iran, presenting Tehran with a choice between getting access to peaceful nuclear energy, or risking isolation with its current nuclear strategy, which he said posed a clear threat.
"As long as the threat from Iran exists, we will go forward with a missile defence system," he said.
European pledges
His wide-ranging speech - which also touched on the need for a united approach to combat the global financial crisis and climate change - was rapturously received by the crowd.
The Obamas received a warm welcome from the Prague crowd
Later Mr Obama met EU leaders for discussions on issues such as climate change and energy security.
He then flew to Turkey for the final stop of his European tour.
On Saturday, Mr Obama attended the Nato summit in Strasbourg, where he secured pledges from European nations to send more troops to Afghanistan to provide security for elections in August.
Mr Obama's first trip to Eastern Europe, 20 years after the end of the Cold War, was supposed to be the highlight of the Czech presidency of the EU.
But his official engagements there have been scaled down in the wake of Prime Minister Mirek Topolanek's resignation late last month, after losing a no-confidence motion.
Mr Topolanek - who has also described Mr Obama's stimulus plan as "the road to hell" - will remain in office until a new cabinet is appointed or fresh elections are held.
STRATEGIC NUCLEAR WARHEADS AROUND THE WORLD
All numbers are estimates because exact numbers are top secret.
Strategic nuclear warheads are designed to target cities, missile locations and military headquarters as part of a strategic plan.
Israel
Israeli authorities have never confirmed or denied the country has nuclear weapons.
North Korea
The highly secretive state claims it has nuclear weapons, but there is no information in the public domain that proves this.
Iran
The International Atomic Energy Agency reported in 2003 there had been covert nuclear activity to make fissile material and continues to monitor Tehran's nuclear programme.
Syria
US officials have claimed it is covertly seeking nuclear weapons.
One-Minute World News
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Obama is a seducer, in the nicest possible way of course. He smiles and refers to himself as Hussein and does all the other things that make Europeans swoon
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