“You have so many countries already — China, Pakistan, you have so many countries, Russia — you have so many countries right now that have them,” he said. “Now, wouldn’t you rather, in a certain sense, have Japan have nuclear weapons when North Korea has nuclear weapons?” A senior Japanese government official quickly reiterated that it was Japan’s policy never to possess nuclear weapons.

On Friday, Mr. Obama described the alliance with Japan and South Korea as “one of the cornerstones of our presence in the Asia-Pacific region” — one that was paid for with the sacrifices of American soldiers during World War II, one that has expanded American influence and commerce and one that “has underwritten the peace and prosperity of that region.”

“You don’t mess with that,” Mr. Obama added.

In summarizing the accomplishments of the Nuclear Security Summits — this was the fourth and final one of his presidency — Mr. Obama acknowledged a tension between his emphasis on nonproliferation and the American military’s relentless efforts to improve the efficiency of its existing stockpile of nuclear warheads. These American technological advances rattle Russia and China, which cite them as a pretext to develop their own new weapons.

“I’ve tried to strike the proper balance,” Mr. Obama said. He noted that he had tried to negotiate a further round of arms reductions with Russia after the New Start treaty. But the return to the presidency of Vladimir V. Putin ended those prospects. In the meantime, he said, the United States needed to make sure its stockpile was “safe and reliable.”

Mr. Putin boycotted this meeting, which foreclosed the possibility of ambitious agreements, since Russia is one of the world’s two largest nuclear-weapons states, along with the United States.

Earlier on Friday, Mr. Obama argued that his marquee accomplishment in nonproliferation — the nuclear deal with Iran — had “achieved a substantial success.” Because of restrictions that the deal imposed on Iran’s nuclear program, he said, it would now take the Iranians about a year to build a bomb — if it breached the deal — as opposed to two to three months before the diplomatic effort began in mid-2012.

Photo President Obama with Prime Minister Shinzo Abe of Japan at the Nuclear Security Summit on Friday in Washington. Credit Doug Mills/The New York Times Asked about reports that the Treasury Department would allow Iran to conduct transactions in United States dollars, Mr. Obama did not answer directly, but suggested that Iran could get access to American banking markets indirectly through European banks. The reports have drawn sharp criticism from lawmakers, including the House speaker, Paul D. Ryan, who urged the White House not to go ahead.

Beyond that issue, Mr. Obama said Tehran could attract more American businesses by adhering not just to the letter of the nuclear deal but to its spirit, which meant not shipping missiles to the militant group Hezbollah, or otherwise destabilizing the region.

The attacks in Brussels and Paris led the president to add a session on terrorism and nuclear security. After banishing reporters and cameras from the room, he showed the leaders a video depicting a terrorist attack in a city involving a nuclear device. Afterward, the leaders discussed how they would handle such an attack.

“Fortunately, no terrorist group has yet succeeded in getting their hands on a nuclear device,” Mr. Obama told them beforehand. “Our work here will help ensure that we’re doing everything possible to prevent that.”

The meeting generated a list of announcements, including the reduction of stockpiles of highly enriched uranium in a variety of countries, including Poland and Kazakhstan, and an agreement to remove separated plutonium from Japan. The nature of these gatherings is that each nation brings along its “gifts,” or proposed offerings, and American officials say that having the leaders all show up for the summit meeting creates a forcing mechanism to get that work done.

But there are also moments that reveal behind-the-scenes disagreements, and one was evident Friday with Japan.

The energy secretary, Ernest J. Moniz, appeared with a senior Japanese official to celebrate the removal of half a ton of highly enriched uranium and separated plutonium, which was shipped to the United States. But the two men took no questions, leaving the Japanese unchallenged about the fact that they are moving ahead on a new plutonium reprocessing plant that should produce up to eight tons of plutonium each year.

That raises concern that Japan will sit on a large supply of nuclear fuel, always a source of tension with its neighbors. Francie Israeli, an Energy Department spokeswoman, said that Japan had removed some of the most sensitive materials and that “we understand that they intend to balance any future reprocessing activities with consumption or disposition.” 

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