When Japanese Prime Minister Shinzo Abe meets with President Barack Obama on Friday in Washington, he will be seeking to press not one but three reset buttons. The United States has a big stake in at least two of his goals — and it’s within Obama’s power to help realize them.

Abe hopes to put back on track a U.S.-Japan relationship frayed by political instability in his country, which has rotated prime ministers every year since 2006.

He hopes to kick-start Japan’s economy, transforming the country from aging, ailing ex-champion to dynamic contributor to the coming Pacific century.

Both of those are essential to Abe’s third goal: resetting his own reputation, which was not enhanced by his first, brief turn as prime minister in 2006-07.

Abe’s legacy is of little concern to most Americans. But as the U.S. seeks to contend — on a limited budget — with a rising China, the ability of its most important Asian ally to contribute, and to serve as a positive democratic role model, matters a great deal.

Abe is Japan’s first leader since 1949 to be given a second chance in office, he reminded me and The Post’s Chico Harlan during an interview here late last week, and he seems determined to take advantage. “I did learn from many mistakes,” he said.

When I interviewed Abe in 2006, he talked grandly of developing a new national identity at home and pursuing a “freedom agenda” abroad. This time more pragmatism is evident. Abe still thinks Japan should promote democratic values abroad, he told us. But his first voyage this time took him not only to democratic Indonesia and Thailand but also to communist Vietnam, suggesting as much interest in countering China as in promoting freedom.

Since his election Dec. 16, he has steered largely clear of the World War II revisionism that motivates the jingoistic wing of his Liberal Democratic Party but infuriates Koreans, Chinese and other Asians. In the interview, he said he would like to leave such matters “to the good hands of historians and experts.”

More to the point, he told us that he learned from his truncated first term to focus on clear priorities, which means the economy and the alliance. Strengthening ties with the U.S., he said, is essential to countering the growing assertiveness of China, which is challenging Japan’s control of disputed islands in the East China Sea.

“It is important for us to have them recognize that it is impossible to try to get their way by coercion or intimidation,” he said. “In that regard, the Japan-U.S. alliance, as well as the U.S. presence, would be critical.”

Meanwhile, aggressive monetary easing and stimulus spending have brightened Japan’s mood; Abe is the first prime minister in a long time whose popularity has risen after his election.

But the effect of “Abenomics,” as it’s been dubbed, may be short-lived or even counterproductive, given Japan’s huge debt, if Abe doesn’t soon fill in the blanks of the most difficult chapter of his economic plan: restructuring and reform.

One step would promote both goals: joining negotiations on the Trans-Pacific Partnership (TPP), a multinational trade agreement that Obama hopes to complete this year. The pact includes nations as varied as Canada, Chile and Brunei but not, so far, Asia’s biggest economies: China and Japan.

Obama envisions a new-model trade deal, setting high standards for dealing with labor and the environment, controlling corruption, and more. It’s not aimed at China, all participants insist. But it is intended to offer an alternative to China’s Communist-controlled capitalism; China won’t be joining any time soon.

Japan could join, boosting the non-military side of its partnership with Washington and energizing reform by subjecting the economy’s most coddled sectors to international competition.

For Abe, the latter is both prize and poison. He came to power by winning Lower House elections, but Upper House elections this summer are crucial to his hope of breaking the one-year jinx that he initiated six premierships ago. To win, his party will need support from farmers and other special interests most threatened by free trade.

Abe said he wants to discuss the TPP with Obama and then decide based on national, not party, well-being. He sounded like someone looking for a way in.

“I believe that a free trading environment would be in Japan’s interest,” he said. “And I believe we need to capture and incorporate the growth potential in Asia for the growth of Japan going forward.”

None of the TPP countries is going to give Japan special exemptions, and U.S. officials have been ambivalent about including Japan’s notoriously tough negotiators in the first round of talks.

But a Japan back on the growth track would be vastly in America’s strategic interest. Obama can frame Japan’s options in ways that might ease Abe’s political dilemma. That would help Abe do what’s best for Japan, and for the alliance, too.

Fred Hiatt is The Washington Post’s editorial page editor. This article is based on an interrview he conducted with Prime Minister Shinzo Abe in Tokyo.