President George W. Bush had a splendid relationship with Japan and its Elvis-loving prime minister, Junichiro Koizumi. Bush never clicked with South Korea’s left-leaning president.

You might think the stars would align the same way for Obama, because during most of his presidency Japan has been led by a left-leaning party and South Korea by a conservative.

But in fact, Obama established a solid working relationship with the pro-American and pragmatic president of South Korea, Lee Myung-bak, while experiencing little but frustration as prime ministers come and go on an annual basis in Tokyo.

So when I sat down this week with the latest Japanese foreign minister, Koichiro Gemba, on his first official visit to Washington, I asked whether Japan’s political merry-go-round might be slowing.

He laughed and said, “I hope we will continue serving for the next three, four or five years.”

Gemba blamed the instability on what Japanese call the “twisted” Diet — an upper house controlled by the opposition party, which makes it hard for the ruling Democratic Party of Japan, with a lower-house majority, to get anything done.

“I believe the future depends on when the two parties learn to cooperate to address the national interest and the public interest,” Gemba said, politely neglecting to point out that Washington doesn’t have much to teach in that department.

Gemba said that Prime Minister Yoshihiko Noda, the third DPJ leader since the 2009 election that ended a half-century of conservative rule, has taken on two arduous goals:adopting a consumption tax to reduce the nation’s mountainous fiscal debt, and exploring Japanese membership in an Asia-Pacific free-trade region. Both ideas arouse fierce opposition, not least from farmers worried about U.S. imports.

“But we are the ones to tackle these issues to overcome populism,” Gemba said. “I believe at some stage the general public will recognize the hard work undertaken by the Noda administration.”

The Noda Cabinet also is looking for more stability in foreign policy. When the DPJ took over in 2009, it overcorrected for what many officials saw as a history of kowtowing to the United States with a tilt to China that alarmed not only Obama administration officials but many Japanese too.

Gemba told me that Japan needs to “deepen our alliance with the United States in a robust engagement, but also we need to engage China. . . . Our interest is not to encircle China.” He proposed to Secretary of State Hillary Clinton a three-way “strategic dialogue.”

Gemba said his second principal goal is to “overcome the recent inward-looking trend in Japan,” typified by a 50 percent reduction in foreign aid over the past 14 years. He noted that Japan’s population of 128 million is projected to fall below 100 million by 2040. So regional and international cooperation will become ever more essential, he said.

“We need to go outward and step forward,” he said.