"The person who made the statements doesn't know much about foreign policy or nuclear policy or the Korean Peninsula or the world generally," Obama said at a news conference at the close of the Nuclear Security Summit.
Obama described the U.S. nuclear umbrella for Japan and South Korea, in place of their own arsenals, as "one of the cornerstones of our presence in the Asia Pacific," which has provided the U.S. peace, prosperity and flowing commerce.
"It has prevented the possibilities of a nuclear escalation and conflict," he added. "You don't mess with that. It's an investment that rests on the sacrifices that our men and women made" in World War II.
He concluded, "We don't want someone in the Oval Office who doesn't recognize how important that is."
The summit came as the Republican front-runner to replace Obama in the White House made several controversial nuclear proposals this week.
Trump said that nuclear proliferation is the world's biggest challenge, but also suggested at a CNN town hall on Tuesday that it may be time for Japan and South Korea to develop their own nuclear arsenals so the U.S. can pull back from Asia.
Japanese Foreign Minister Fumio Kishida squelched the idea of his country developing its own nuclear weapons, saying, "It is impossible that Japan will arm itself with nuclear weapons."
The island nation is the only country to experience a nuclear attack, when the U.S. ended World War II by dropping bombs on Hiroshima and Nagasaki, and has been committed to a non-nuclear defense posture since then.
Trump has also suggested redrawing U.S. security relationships in other regions, arguing that Germany and Saudi Arabia need to do more in their own defense or pay the U.S. more for the protection it offers.
And he's proposed using nuclear weapons to put a swift and definitive end to the threat of ISIS.
"I would never take any of my cards off the table," Trump told MSNBC.
The summit, the final of four Obama has held during his presidency, drew leaders from around the world to discuss ways to prevent the use of nuclear weapons and better secure nuclear materials, especially from the threat of nuclear terrorism.
Obama said global efforts to improve nuclear security have removed from circulation material that is equivalent to 150 nuclear weapons, safeguarding it from extremists.
"That's material that will never fall into the hands of terrorists," Obama said.
Non-proliferation efforts mean the entire continent of South America is free of nuclear materials. If Poland and Indonesia meet commitments this year, Central Europe and Southeast Asia will follow suit, he said.
"As terrorists and criminal gangs and arms merchants look around for deadly ingredients for a nuclear device, vast regions of the world are now off-limits, and that's a remarkable achievement," he said, admitting that much work remains.
Obama said that while leader-level summits are ending, the delegates have agreed to create a new nuclear security contact group of more than 30 countries to institutionalize their work and build on their achievements.
Obama said he realized that "our vision will not happen quickly, perhaps not in my lifetime, but we have begun."
He noted that nuclear stockpiles are the lowest they've been in six decades. "I'm extremely proud of our record," he said.
The summit focused particular attention to ISIS, devoting a special session to the group, which has demonstrated an interest in nuclear materials, Obama said. After the Paris attacks in November, investigators found hours of footage tracking the movements of a Belgian nuclear official.
Obama said earlier Friday that it was likely that as the anti-ISIS coalition continued to make gains against the terrorist group, the organization would try to conduct more attacks outside the Middle East.
"As ISIL is squeezed in Syria and Iraq, we can anticipate it lashing out elsewhere, as we've seen most recently and tragically in countries from Turkey to Brussels," Obama said Friday, using another acronym for ISIS.
At the opening of the nuclear conference's Friday session, Obama said the summit's work -- mostly done quietly behind the scenes in the months between high profile gatherings -- served the crucial purpose of reducing the chances that nuclear materials could be stolen.
"The single most effective defense against nuclear terrorism is fully securing this material so it doesn't fall into the wrong hands in the first place," Obama said.
He called on the attending countries -- more than 50 -- to improve intelligence sharing and do more to cut off the flow of foreign fighters going to Syria and Iraq.
"The sense of urgency that we've shown in destroying ISIL in Iraq and Syria also has to infuse our efforts to prevent attacks around the world," Obama said. "We simply cannot afford to have critical intelligence not being shared as needed, whether between governments or within governments."
The summit meeting offered an opportunity to "explore ways to step up those efforts," Obama said.
Over the four meetings that have taken place since 2010, the nations involved have made 260 commitments to improve nuclear security and implemented three-quarters of them, the president said.
Nuclear non-proliferation has been a focus for the President since his days as a junior senator from Chicago. He co-wrote legislation on nuclear controls and travelled to inspect safety measures at nuclear sites in Eastern Europe and Russia while in the Senate.
Much of the nuclear summit's work has focused on reducing countries' levels of highly enriched uranium or improving training for handling nuclear materials.
Critics have said that the efforts fall short because discussions haven't focused on military stockpiles of highly enriched uranium or civilian plutonium, seen by resource-poor countries as a potential source of energy.
And they point to Russia's decision not to send high-level representation as a setback, given that the U.S. and Russia between them control the vast majority of nuclear materials.
But Obama claimed progress Friday, announcing that 102 nations have ratified what he called "a key treaty," a Convention on the Physical Protection of Nuclear Material which will enter into force in coming weeks.
That, Obama said, gives "us more tools that we need to work together in the event of theft of nuclear material or an attack on a nuclear facility."
Leaders wrapped up the meeting with a communique that pledged to use the foundation built during the four summits to guide future work.
"Sustaining security improvements requires constant vigilance at all levels, and we pledge that our countries will continue to make nuclear security an enduring priority," the statement said.