When President Yoon Suk Yeol of South Korea visited the White House last year, he charmed the Washington establishment by singing Don McLean’s “American Pie.” When he flew to Tokyo to usher in a new era of conciliation with Japan, it was a genial visit, with the prime minister treating Mr. Yoon to “omurice,” a Japanese dish that the South Korean leader likes.

But that mood was gone on Wednesday, a day after Mr. Yoon imposed — and then rescinded — martial law in South Korea. Officials in the United States and Japan were scrambling to understand why the leader they’d both embraced had made such a shocking authoritarian move.

Now, the domestic political chaos unleashed by Mr. Yoon could imperil the countries’ three-way alliance in the Pacific, where they had been fortifying their relationships to confront an increasingly assertive China and North Korea.

The disorder in South Korea — where cabinet members on Wednesday were offering to resign and opposition lawmakers were moving to impeach Mr. Yoon — comes on top of political uncertainty in both the United States and Japan. Last month, former President Donald J. Trump, a notoriously mercurial leader who tried to undermine American alliances while in power, was elected to a second term.

And in October, Japanese voters delivered a resounding blow to the longtime governing party and the new prime minister, Shigeru Ishiba, denying them a majority in Parliament.

“Many in the world were counting on Japan and South Korea, along with Australia and others, to keep the flag flying and keep the head of good governance and democracy above water in the face of this incredible pressure from North Korea, China and Iran and Russia,” said Daniel Russel, a vice president at the Asia Society who was the assistant secretary of state for Asia under President Barack Obama.

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