Mikheil Saakashvili, Georgia's president, told Al Jazeera that the threat of nuclear material falling into the wrong hands was very real.
He said his government had disrupted a number of smuggling attempts of nuclear material through Georgian territory.
"That is an issue, because you get these black holes that are not subject to any international regimes... people can move back and forth quite freely, and there are no real security services to control that," he said.
Tuesday's declaration is not legally binding, with no mechanism to enforce the measures.
Rob Reynolds, Al Jazeera's senior Washington correspondent, said it would be another two years before there was any proof that nations have lived up to their commitments.
"In 2012 the next nuclear security summit will be held in South Korea," he said.
Still, Obama defended the agreement, saying he believed world leaders were taking their commitments on what he called the world's top security threat, seriously.
"Today is a testament of what is possible when nations come together in a spirit of partnership to embrace our shared responsibility and confront a shared challenge," Obama said at a news conference at the end of the summit.
Leaders recognised the "urgency and seriousness of the threat" of non-state actors and thus had to make actions that are "bold and pragmatic", he added.
Joel Rubin, the deputy director and chief operating officer at the National Security Network, a non-governmental organisation that focuses on US national security and foreign policy, hailed the pledges made during the summit.
"What we are seeing is a motivation on the part of countries who have been working on this and are interested in this to come to the table," he told Al Jazeera.
"We have witnessed now a multinational summit that really was outstanding by all accounts.
"The practical challenges are to build on the momentum that came out of the communique, to be sure that the multilateral process does take hold and the countries that made the commitments are living up to those commitments."
The summit was, however, overshadowed by a state actor: Iran.
Al Jazeera's Reynolds, who spoke to several delegates at the two-day summit, said most of the talks on the sidelines of the meeting were about possible sanctions against Iran.
|Obama acknowledged that China still has concerns about sanctions against Iran [EPA]
A day after discussing Iran with Hu Jintao, his Chinese counterpart, Obama expressed gratitude that China had agreed to help negotiate a new UN sanctions resolution on Iran but said Beijing still had concerns about sanctions.
"The Chinese are obviously concerned about what ramifications this might have on the economy generally," Obama said. "Iran is an oil-producing state."
Iran is China's third-largest crude oil supplier.
Obama said last month that he hoped to get a new sanctions resolution ready within weeks.
He did not repeat that timetable on Tuesday but said he did not want a long, drawn-out process that takes months, and that he wants to "see us move forward boldly and quickly".
"I think that we have a strong number of countries on the [UN] Security Council who believe this is the right thing to do. But I think these negotiations can be difficult and I am going to push as hard as I can...," he said.
Focus on non-proliferation
Beijing stressed on Tuesday it wanted any UN Security Council resolution to promote a diplomatic way out of the nuclear standoff.
"The well-being of the Iranian people as well as the normal economic, trade, financial and energy exchanges between Iran and many countries in the world - these legitimate needs and demands should not be undermined," Cui Tiankai, the Chinese vice-foreign minister, told reporters on Tuesday.
In another sign of the limits to co-operation on the issue, Dmitry Medvedev, the president of Russia - another nation that has significant trade with Iran - said any sanctions "certainly must not punish the people" and should focus on non-proliferation.
Yukiya Amano, head of the International Atomic Energy Agency (IAEA), told the Reuters news agency that he was concerned Iran might reduce co-operation with the UN nuclear watchdog's inspectors if further sanctions are imposed on it.
The summit did, however, produce some tangible results. Among bilateral agreements announced was a deal signed by Russia and the US to reduce stocks of excess weapons-grade plutonium.
A follow up summit is planned for 2012 in South Korea.