The US and Russian presidents are at the summit fresh from a new treaty
World leaders at a summit on nuclear security in Washington have heard dire warnings of the danger of nuclear material falling into the wrong hands.
US President Barack Obama, opening the biggest international meeting hosted by the US since 1945, greeted leaders from nearly 50 countries.
Officials said more should be done to prevent theft or smuggling.
Meanwhile, France's leader stressed his country could not give up its own nuclear weapons.
The US welcomed a Ukrainian pledge to eliminate its stockpile of highly enriched uranium by 2012.
The two-day summit is taking place without representatives of Iran and North Korea, neither of whom were invited by the US because of the disputes over their nuclear programmes.
Israeli Prime Minister Benjamin Netanyahu dropped plans to attend the summit, reportedly because of concern that Muslim states planned to press for Israel to open its own nuclear facilities to international inspection.
'Proliferators not welcome'
The head of the International Atomic Energy Agency, Yukiya Amano, said that nuclear powers needed to do more to protect nuclear materials.
"The problem is that nuclear material and radioactive material are not well protected and member states need to better protect these materials against the theft or smuggling," he told the BBC.
"On average every two days we receive one new information on an incident involving theft or smuggling of nuclear material."
UK Foreign Secretary David Miliband said that nuclear nations like Pakistan were vulnerable.
"The message from this summit is that any country can be treated as a normal country on nuclear matters if it behaves like a normal country," he said.
"Proliferators are not welcome in the modern world, nuclear proliferators especially, and I think it's a very clear message to the Iranians and others that there is an international desire to use civilian nuclear power for beneficial purposes, but not to allow it to leech into a military weapons programme that could be so dangerous, especially in a region like the Middle East."
A senior American counter-terrorism expert, John Brennan, warned that al-Qaeda had been seeking material for a nuclear bomb for more than 15 years.
"There have been numerous reports over the past eight or nine years of attempts to obtain various types of purported material," he told reporters.
"We know al-Qaeda has been involved a number of times. We know they have been scammed a number of times."
President Obama and his Chinese counterpart Hu Jintao held pre-summit talks on Iran.
"The Chinese very clearly share our concern about the Iranian nuclear programme," said Jeff Bader, Mr Obama's senior director for Asia on the National Security Council.
"The two presidents agreed the two delegations should work together on a sanctions resolution in New York."
However, Chinese foreign ministry spokeswoman Jiang Yu later said that sanctions "cannot essentially solve the problem".
Ukraine has 160-250kg of highly enriched uranium (HEU) in civilian use
It fuels a research reactor, which will be converted to run on low enriched uranium (LEU)
Ukraine's nuclear power stations run on LEU
The US will provide financial and technical help - it is not yet decided where the HEU will be taken
If it is taken to Russia it will go by rail, if to the US it will be shipped in a double-hulled vessel
The US has helped convert, or shut down, 67 HEU reactors in 32 countries
Sources: NTI, AP
"China supports the dual-track approach and believes that dialogue and negotiations are the best way to appropriately resolve the Iranian nuclear issue," she said.
BBC world affairs correspondent Nick Childs says the US clearly feels it has nudged the Chinese forward on the issue of new sanctions against Iran.
But the more cautious Chinese account suggests that tough diplomacy still lies ahead, with the outcome far from clear, he adds.
Just before the summit opened, Ukraine agreed to eliminate its stockpile of weapons-grade nuclear material which, the US said, was enough to build "several weapons".
It is estimated there are about 1,600 tonnes of highly enriched uranium in the world - the type used in nuclear weapons.
Experts agree that virtually all of it is held by the acknowledged nuclear-weapons states, most of it in Russia.
Speaking in an interview before the summit opened, French President Nicolas Sarkozy said his country would not give up its nuclear weapons because to do so would be to jeopardise national security.
He said: "I have inherited the legacy of the efforts made by my predecessors to build up France as a nuclear power and I could not give up nuclear weapons if I wasn't sure the world was a stable and safe place."
Last week, the US and Russia signed a new Strategic Arms Reduction Treaty, reducing each country's deployed nuclear arsenal to 1,550 weapons.
Mr Obama has also approved a new nuclear policy for the US, saying he plans to cut the nuclear arsenal, refrain from nuclear tests and not use nuclear weapons against countries that do not have them.