Japan’s newly elected Prime Minister Shinzo Abe made his first overseas visit to Southeast Asian countries. Very soon he will make the more usual pilgrimage from Tokyo to Washington to meet U.S. President Barack Obama.

What should he say to Obama as both begin their new terms in office? On what issues do other Asians hope the two long-standing allies will focus?

The expectation — or fear — is that the conversation will turn to the other Asian giant not in the room: China.

The Obama administration says its pivot to Asia is to engage the most dynamic region in a depressed world. Partly. But it is not only the paranoid in Beijing who believe that competition with China has been a factor.

For Japan, the Abe administration is making its own pivot to focus on the Association of Southeast Asian Nations (ASEAN). This comes as Sino-Japanese tensions over the Senkaku/Diaoyu islands have boiled over in the recent months — with street riots, scrambling jets and incursions at sea.

With such developments, some predict the Obama-Abe conversation will focus on ways to mobilize their long-standing alliance to deal with Beijing. The South China Sea would be a hot topic. Manila — also an American ally — has challenged China and the Abe administration has now promised to supply them with coastal patrol vessels.

With that and the Senkaku dispute, there is concern that Abe — long seen as hawkish — returns from America with a deputy sheriff’s badge.

Asians should hope otherwise. There is an alternative and pressing agenda.

Obama has set out legislative ambitions that will require time and effort back home, and not adventures in Asia. It’s critical that the U.S. economy — showing some positive signs — be set firmly on track to full recovery. This can help ease difficult questions about the deficit and provide momentum to other promised changes. More, the reality is that renewed economic vigor must be the foundation for America’s long-term commitment and esteem in Asia.

Similarly, Abe faces domestic challenges. His “Abenomics” — a yen version of America’s quantitative easing — is controversial medicine. But there is more optimism than there has been for years, as share prices in Tokyo show.

Abe should build on this mood, and aim to win the Upper House election this coming summer. Victory could mean a longer stay than recent predecessors — who lasted little more than a year.

Security talk is of course necessary and the United States and Japan could usefully discuss how and to what extent either will respond to provocations and a possible incident at sea. But an anti-Chinese cabal is not inevitable.

The two leaders need to develop mutual understanding on economic policies. As the yen softens, the Abe administration needs to assure Americans that this won’t go too far and trigger competitive devaluations. The two leaders also need to discuss the Trans-Pacific Partnership (TPP).

The TPP is a key Obama initiative to integrate nine countries across the ocean and Japan’s entry could add considerable heft to the group.

But the aim is for completion by end 2013 and it is unclear whether Japan wants to come on board, and would be welcome. The idea, floated under the preceding Democrat Party of Japan governments, must take into account the TPP’s ambitious targets, especially in agriculture. Abe’s Liberal Democratic Party has usually protected this sector to maintain rural support and some observers suggest his hands are tied.

Yet accepting the TPP could anchor the structural reforms that Japan needs. Without such disciplines, Abenomics might — like previous administrations — throw money at white elephant projects and infrastructure.

Even when security issues are discussed, there are hopes that China and Japan will contain their differences. Beijing has hosted the New Komeito party leader — junior partner in Japan’s ruling coalition — and the door is open for Abe and new Chinese leader, Xi Jin Ping, to meet.

Neither side can give up its claims but stoking up conflict would hurt them both. The world economy is in a poor health and Japanese leaders would do well to find ways to live with China — with whom there is deep economic interdependence.

If that is what Abe says to Obama, he might well find America faces similar issues. And if both the U.S. and Japan agree there are good reasons and possible ways to maintain a steady relationship with a growing China, that would reassure the region.

Simon Tay is chairman of the Singapore Institute of International Affairs and teaches international law at the National University of Singapore. He is the author of “Asia Alone: The Dangerous Post Crisis Divide from America.”

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