"More nations have acquired these weapons, tests continue ... the knowledge to build these weapons has spread.
"If we say to ourselves that the spread of nuclear weapons is inevitable we are saying that the use of nuclear weapons is inevitable."
Obama, in Prague as part of an eight-day visit to Europe, was due to travel to Turkey later on Sunday.
Nuclear energy bank
Obama said the US will seek ratification of the comprehensive test ban treaty on nuclear weapons.
He proposed a nuclear energy bank that nations could access to meet their requirements. The banks in turn would prevent them from using other nuclear materials that could potentially be used to make bombs.
He said that nations should have access to nuclear power for peaceful reasons to combat climate change and to allow people a way out of poverty.
Obama also said that the US would host a summit to discuss the "locking down" of loose nuclear materials, before the end of the year.
In reference to North Korea and Iran, he said that nations who break the rules of nuclear proliferation must be punished.
He said that if Iran continued with its nuclear programme, which many suspect is for weaponry rather than Tehran's stated goal of nuclear energy, the US would build a proposed missile defence shield in Eastern Europe.
'If the Iranian threat is eliminated we will have stronger basis for security and the driving force for missile defence construction in Europe will be removed," he said.
Obama's speech came hours after North Korea launched a satellite into orbit on a rocket that has the capacity to carry nuclear warheads long-range.
Rob Reynolds, Al Jazeera's correspondent in Prague, said: "He's going to try to lead by example ... and rally international support for renewed anti-nuclear weapons steps.
"More concretely he is going to, and has already begun engaging the Russians to restart nuclear arms reduction and limitation talks with a view towards having a treaty on that subject completed before the end of the year."
Obama also urged the EU on Sunday to accept Turkey as a full member of the 27-nation bloc, a move immediately rejected by Nicolas Sarkozy, the French president.
The disagreement was a rare sign of divergence at an EU-US summit stage-managed to relaunch transatlantic ties, strained under the administration of George Bush, the former US president.
"The United States and Europe must approach Muslims as our friends, neighbours and partners in fighting injustice, intolerance and violence, forging a relationship based on mutual respect and mutual interests," Obama told the summit.
There are an estimated 24,000 nuclear weapons in the world
Russia owns 13,000 of the world stocks
The US has around 10,000
France, China and the UK also have stocks
Pakistan and India have nuclear weapons but are not members of the nuclear non-proliferation treaty
Israel is believed to have nuclear weapons but refuses to discuss its capabilities
"Moving forward towards Turkish membership in the EU would be an important signal of your [EU] commitment to this agenda and ensure that we continue to anchor Turkey firmly in Europe," he told EU leaders.
Turkey has long been seeking to join the bloc, and Obama's comments were a reaffirmation of US support for that goal.
But there has been resistance among EU states such as Germany and France to its membership.
Sarkozy said it was up to the EU member states to decide on Turkish entry and reiterated his opposition.
"I have always been opposed to this entry," he told France's TF1 television on Sunday.
"I still am and I think I can say that the immense majority of member states shares the position of France.
"Turkey is a very great country, an ally of Europe, an ally of the United States. It will stay a privileged partner. My position hasn't changed and it won't change."
Anita McNaught, Al Jazeera's correspondent in Ankara, said: "Turkey's accession process could go on till 2020 and beyond. Recent provincial elections suggest the Turkish public is keen for Turkey to put more effort into the EU venture.
"But there is national pride too. If the EU keeps pushing back, there are many people in Turkey saying: 'Well, why should we bother?'"