But I wonder if he should instead have visited just two countries, China and Japan. That’s where the most significant and dangerous new developments in international relations are unfolding. The world’s second- and third-largest economies have been jostling for months over territory, reviving ugly historical memories and making clear that, in the event of a crisis, neither side will back down. Trade between the two countries — which usually hovers around $350 billion a year — is down substantially. An accident, miscalculation or unforeseen event could easily spiral out of control.

All this is happening in the context of a China that is changing, internally and externally, one that lacks a deep and strategic relationship with the United States. In fact, the lack of progress in relations with China stands as the largest vacuum in President Obama’s generally successful foreign policy.

This has not been for lack of effort. The Obama administration came into office determined to make Asia a priority, topped by its ties to China. Hillary Clinton’s first trip as secretary of state was to Asia, and she signaled that discussions with China would focus on large strategic issues and not get bogged down over human rights. The administration wanted to engage China as a partner of sorts. Zbigniew Brzezinski, known to be close to President Obama, speculated about the need for “G-2” — an ongoing dialogue between Washington and Beijing on the big challenges facing the world.

China’s reaction to these overtures was confused and muddled. Beijing worried that it was being asked to involve itself in superpower diplomacy, which would distract it from its single-minded focus on economic development. China wanted to protect its right to be considered a developing country so that, for example, it could continue to industrialize without too much regard for climate change. Some in the Beijing foreign-policy elite wondered if this was a trap, forcing their government to rubber-stamp decisions that would be shaped and directed out of Washington. Others saw the Obama administration’s overtures as a sign of China’s growing strength, convincing them that the best path for Beijing was to keep building up economic strength and bide its time.

As a result, Beijing’s response to the administration’s initial diplomacy was cool. At the 2009 Copenhagen climate change conference, it was even dismissive and combative, actively trying to oppose U.S. efforts to reach a consensus.

Meanwhile in Asia, many of the continent’s other powers had begun worrying about a newly assertive China. From Japan to Vietnam to Singapore, governments in Asia signaled that they would welcome a greater American presence in the region, one that would assure them that Asia was not going to become China’s back yard.

The Obama administration shrewdly responded with its “pivot” in 2011, combining economic, political and military measures, all designed to signal that the United States would strengthen its role in Asia, balancing any potential Chinese hegemony.

The result of the pivot, however, was to further strain relations with Beijing. Today China and the United States maintain mechanisms, such as the strategic and economic dialogue between senior officials, but they are formal and ritualistic. No American and Chinese officials have developed genuinely deep mutual trust. Beijing views the pivot as a containment strategy and believes that rising Japanese nationalism — tolerated by Washington — is responsible for the crisis in the East China Sea.

Japan does seem to be entering its own more assertive phase, for domestic reasons. But the larger shift lies in Beijing. China has become the dominant power in Asia. Simultaneously it is going through economic challenges, as the heady growth strategy of prior decades faces obstacles, and a complex political transition. Elements of the Chinese establishment, such as the People’s Liberation Army, have wanted a tougher line toward the United States. The revelations about Chinese government-sponsored hacking of U.S. defense and corporate secrets fit into this general picture of China becoming more forceful and arrogant.

Whoever is to blame, the fact remains that the only durable path to stability in Asia is a strong relationship between the United States and China. The two countries are not always going to agree, but they need to have much better and deeper ties.

When he gets back from his trip, Secretary Kerry should start planning his next one, to Asia.