WASHINGTON - Barack Obama this week makes his first trip to Asia as president, leaving behind a host of domestic problems with a visit that recognizes the region's economic and diplomatic importance to the United States.

The trip, which starts on Thursday, will take Obama to an Asia-Pacific Economic Cooperation (APEC) summit in Singapore.

But the critical leg will come in China, where Obama will have to navigate an increasingly complex relationship with the country that is the largest holder of U.S. foreign debt and its second-largest trading partner.

I see China as a vital partner, as well as a competitor, Obama told Reuters in an interview before the trip.

The key is for us to make sure that that competition is friendly, and it's competition for customers and markets, it's within the bounds of well-defined international rules of the road that both China and the United States are party to, but also that together we are encouraging responsible behavior around the world, he said.

He will also visit Japan and South Korea.

The overarching theme is that America is a Pacific nation, it understands the importance of Asia in the 21st century, and it's going to be very engaged in a very comprehensive way to make progress on a whole series of issues that are critical for our prosperity and our security, said Ben Rhodes, a deputy national security adviser.

North Korea, Iran, the global economy and trade, climate change, energy, human rights, Afghanistan and Pakistan are likely to get the most attention. Obama will also use a stop in Tokyo to speak broadly about his view of U.S. engagement with Asia.

In China from November 15-18, Obama will visit Shanghai and Beijing, hold bilateral meetings with President Hu Jintao -- their third -- and Premier Wen Jiabao.

DEEPLY ENGAGED

The trip is intended to make the point that the United States is deeply engaged with Asia, after years of focusing on the threat of Islamic militancy in the region.

But the issues dominating U.S. politics -- his fight to reform the healthcare system, joblessness and the pressing question of how many more troops to send to Afghanistan -- are likely to dog Obama on his Asian trip.

Those domestic worries could make it more difficult to make progress on climate change and trade, on which he faces stiff opposition from U.S. groups whose support he needs on healthcare and other issues.

Many businesses, for example, are wary of new rules on climate change they say could be costly and labor unions worry about free trade agreements they fear could cost jobs, so Obama is unlikely to push hard for deals such as a free trade pact with South Korea.

I think the administration has been sending pretty careful signals that, hey, we're not gone on trade ... we'll be back to the table on trade on some of these regional agreements and some of the bilateral agreements, said Ernie Bower, director of the Southeast Asia program at the Center for Strategic and International Studies in Washington.

Do Asian leaders believe that? I'm not sure, he said.
With Obama enjoying sky-high popularity ratings in the countries he is visiting, concrete results may be beside the point. Noting that Obama has been in office only since January, analysts and administration officials point to this trip as mostly laying the groundwork for future cooperation.

President Obama is enormously popular in all the countries that he's visiting. I haven't seen the latest polls, but the numbers I have seen are staggering, said Jeffrey Bader, senior director for East Asian affairs at the National Security Council.

When we have someone who has that degree of respect and affection and admiration, the message that he is bringing is much more likely to resonate than when you come in with a five percent approval rating, he said.

(Additional reporting by Caren Bohan, editing by Chris Wilson)