SEOUL — The gathering of leaders of the NATO nations at Madrid provided an ideal setting for a portentous trilateral summit on an overwhelming issue thousands of miles away.

While the war on Ukraine had to be the more pressing concern for NATO,  President Biden and the leaders of America’s two northeast Asia allies, Prime Minister Fumio Kishida of Japan and President Yoon Suk-yeol of South Korea,  focused on the North Korean nuclear threat.

It marks the first trilateral summit for America, Japan, and South Korea in nearly five years and the first time the Japanese and South Korean leaders had been invited to attend the NATO sessions as observers.

This summit was strictly on the sidelines, but the message was clear: All three should stick together in a unified response if North Korea’s Kim Jong-un orders the North’s seventh nuclear test, and they should also cooperate on joint military exercises.

Mr. Yoon also had the chance to plead for NATO support in a speech between addresses by Britain’s prime minister, Boris Johnson, and Mr. Biden.

“The international community,” he said, “must show clearly” that its collective desire to denuclearize North Korea is stronger than the North’s “reckless will to develop nuclear weapons and missiles.”

In a rebuke of China and Russia for blocking Security Council resolutions after North Korean missile tests, he decried them as “a clear violation of Security Council resolutions.”

Although Japan’s record as a colonial power in Korea up to the end of World War II precludes an alliance with South Korea, the fact that their leaders saw the NATO session at Madrid as a chance to meet and talk showed the depth of their shared worries about the North.

North Korea’s nuclear and missile threats are “becoming more sophisticated,” Mr. Yoon said,  and “the importance of cooperation between South Korea, the U.S. and Japan has become even greater.” 

A South Korean official quoted by Yonhap, the South Korean news agency, said Mr. Yoon would call for a strong response to North Korean “provocations” in the form of “close cooperation between South Korea, the U.S., and Japan.”

Mr. Kishida displayed Japan’s desire to work with South Korean as well as American forces, urging a response “at a trilateral level” to a North Korean nuclear test. As for Mr. Biden, he was quoted as saying he was “deeply concerned” by the prospect of another such test.

If the words sounded less than stirring, Mr. Biden had to be pleased that the leaders of Japan and South Korea could sit down in the same room and sort out their problems. He assured both of them during his recent visits to Seoul and Tokyo of America’s support against the North, but there was no chance of a trilateral summit so soon after Mr. Yoon’s inauguration as president on May 10.

The decisions of Messrs. Kishida and Yoon to fly to Madrid reflects the mounting tempo of worries about whatever the North Korean leader, Kim Jong-un, has in mind. A three-day session of the military commission of the ruling Workers’ Party, of which he is general secretary, called for “strengthening deterrence” — language that suggested North Korea might place short-range missiles laden with tactical nuclear warheads close to the line with South Korea.

“North Korea is ready at any moment to conduct a nuclear test,” the South’s unification minister, Kwon Young-se, told journalists for foreign news organizations Monday. “What is left is a political decision.”

The inference was that Mr. Kim is awaiting the most propitious moment. “They intend to maximize the impact of any nuclear test,” he said.

North Korea has test-fired numerous missiles this year but has not conducted a nuclear test since September 2017, when Donald Trump was president. Mr. Kim held off on testing nukes during a period in which he met Mr. Trump three times, beginning with their summit at Singapore on June 12, 2018.

Mr. Kim also met three times that year with Moon Jae-in, the liberal South Korean president who was Mr. Yoon’s predecessor. He ignored Mr. Moon’s pleas for another summit after the failure of his summit with Mr. Trump at Hanoi in February 2019, and the North has not responded to recent messages from the South looking for cooperation on flooding during heavy rains.

North Korea has stepped up the rhetoric against both America and South Korea since the election of Mr. Yoon, a conservative who has made relations between South Korea and Japan a top priority.

Mr. Kwon warned that North Korea is just as interested in menacing South Korea as it is in threatening America or Japan. “North Korea is keying on the Korean peninsula,” he said. “To those people who claim North Korea is not aiming at South Korea, you were wrong.”

The prospect of trilateral unity on defense is obviously worrisome to North Korea. Pyongyang’s Korean Central News Agency said America was “hell-bent on military cooperation with its stooges.” The trilateral summit of the American, Japanese, and South Korean leaders, it said, portended “an Asian version of NATO.”

In Pyongyang, an exhibit showed what purported to be atrocities committed by American soldiers, including a soldier murdering a baby with an ax, according to NK News, a website that tracks North Korea from Seoul. NK News also showed an image of a burning child.

NK News quoted Rodong Sinmun, the party paper, declaring “fury and hostility is boiling over toward the sworn enemy.” The paper said America’s “unchanged hostile policy” was “to destroy our country.”