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When Japanese Prime Minister Shinzo Abe meets with President Obama on Friday, 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...