And Mr. Trump brings other kinds of uncertainty, grumbling about Japanese trade barriers and the cost of United States military support, and raising the specter of a more confrontational approach to China that could have unpredictable results in the region.
“Japan is in a kind of a crisis over what direction we can go,” said Kyoji Fukao, a professor of international economics at Hitotsubashi University.
The alliance between Japan and the United States has endured since the end of World War II, but analysts say Mr. Abe, a conservative nationalist, and Mr. Obama, a liberal who had ambitions to change the world, have helped to make the partnership stronger than it has been for decades.
“This is the strongest, most reliable and trusting relationship probably in the last 40 years at least,” said Takatoshi Ito, a professor of international finance and trade at Columbia University. “This has been a good four years.”
Given Mr. Abe’s nationalist leanings, he might not have seemed the most likely Japanese leader to embrace the United States, or a Democrat like Mr. Obama, so warmly.
Yet since he took office four years ago, after an earlier stint as prime minister in 2006-7, Mr. Abe has committed Japan to several policies favored by the Obama administration.
Mr. Abe expanded Japan’s support of United States military bases despite fierce opposition in Okinawa, and pushed through controversial security legislation that allows Japan’s military, the Self Defense Forces, to participate in combat missions abroad. He offered nonmilitary aid to countries battling the Islamic State, even as ISIS militants killed a Japanese hostage.
The clearest motivation for Mr. Abe was the need for a partner in defending against a rising China.
“In the regional geopolitics, I think Japan and the U.S. are both pushed closer to each other by China,” Mr. Ito said. “For security, there is no one but the U.S. which can provide the security to Japan, so there is no question about it.”
Mr. Obama provided very clear promises of protection. In 2014, during a visit to Tokyo, he declared that a security treaty obligated the United States to defend Japan in its confrontation with China over a set of disputed islands in the East China Sea, known in Japan as the Senkaku and in China as the Diaoyu. It was the first time an American president had explicitly said so.
Now Japan’s leaders are warily watching Mr. Trump’s approach to China. They may like that Mr. Trump is taking a more aggressive stance toward Beijing on issues like trade, Taiwan and the South China Sea, but there are also risks for Japan if that stance triggers a hostile response.
“Standing tall vis-à-vis Beijing is of course welcome,” said Sheila A. Smith, a Japan expert at the Council on Foreign Relations. But “the potential for use of force or a much more bellicose U.S.-Chinese relationship would be an uncomfortable spot for Tokyo.”
Partly in hopes of providing another counterweight to China, Mr. Abe has worked for months to develop a relationship with Russia, trying to resolve a dispute over a set of islands that has prevented the signing of a peace treaty since World War II ended. But a recent summit meeting in Japan between Russia’s president, Vladimir V. Putin, and Mr. Abe ended with little progress.
Perhaps an even bigger disappointment for Mr. Abe is Mr. Trump’s vow to pull the United States out of the Trans-Pacific Partnership, on which both Mr. Abe and Mr. Obama spent considerable political capital.
For Mr. Abe, it was in part an excuse to push for changes in Japan’s agricultural industry, as well as an opportunity to gain tariff-free access for Japanese manufacturers to export markets in the United States and elsewhere. Now his only hope is to try to persuade Mr. Trump to resuscitate the deal. Mr. Abe briefly met Mr. Trump in New York in November, and he hopes to see Mr. Trump again in Washington shortly after the inauguration.
Mr. Abe has said he will continue to push for trade deals with other countries, and he is also seeking international partners on other issues. He visited Cuba and talked with the former leader Fidel Castro before he died, asking for Mr. Castro’s help in reining in North Korea’s nuclear program. In October, Japan and Britain conducted their first joint military exercises as part of a move to establish closer security ties in the East and South China Seas.
But the alliance with the United States remains the bedrock of Japan’s security, and none of its leaders are currently considering any other significant alternative. Given that, Mr. Abe and other Japanese officials will work hard to persuade Mr. Trump to maintain a strong partnership.
Some analysts said that may be a matter of education as much as anything else. “We are not sure that he knows the concrete measures or details of U.S.-Japan security relations,” said Fumiaki Kubo, a professor of political science at the University of Tokyo, speaking of Mr. Trump.
“What Prime Minister Abe has to do is give him Lesson 101 on U.S.-Japan relations,” Mr. Kubo said.
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