US-China relations set the tone for East Asia: When they are stable, the region is calm; when they are roiled, the region is uneasy. In time, the same will hold true, I believe, for other regions as well. United States-China relations will certainly be a, if not the, central pillar of any new post-Cold War international order.

US-China relations are mature; it has been 44 years since president Richard Nixon's visit to Beijing transformed the global strategic landscape. US-China relations are intricately interdependent across a broad spectrum of domains. And US-China relations are infused with deep strategic distrust.

The US and China are currently groping towards a new modus vivendi with each other and the rest of East Asia. The complexity of US-China relations and hence the complexity of the adjustments between them are a large part of the uncertainties of our times.

I am not clairvoyant. My purpose here is to sketch some of the issues that will have to be confronted. In particular, I want to deal with the roots of the strategic distrust that exists between them. Unless that is understood and dealt with, no matter how well the US and China may work together on climate change or terrorism or finance or any other specific issue, a stable new equilibrium will be difficult - if not impossible - to achieve. And even if some sort of equilibrium is reached, it will be difficult to maintain.

Despite or perhaps because of their long experience of each other, US-China relations have been rife with misunderstanding. The most persistent in recent times is the notion that economic reform will lead to political reform. American attitudes towards China have oscillated between hopes and fears that perhaps say more about America than China. What is surprising is that despite persistent misunderstanding, there has been so little trouble, although when trouble ensues it has been spectacular, as during the Korean War.

Today, the dominant attitude seems to be drifting towards regarding China as a threat, at least in the American media and political discourse. Perhaps it is. But it is important to understand the nature of the challenge accurately and exaggerating the so-called "China threat" is as bad as wishful thinking. Competition and rivalry are intrinsic parts of relations between all major powers. As China gains strength and confidence, it is bound to pursue its interests more assertively and acquire the instruments to do so. We may consider China's military modernisation as in our interests or see it as against our interests, but China acquiring a modern military is not in itself unusual. Competition is not necessarily conflict. The important question is what use China makes of its growing military strength.

This is not a question that should lend itself to facile answers. US-China relations defy simple characterisation. But it is certainly not "a Clash of Civilisations".

China could not have succeeded without the US. China's success is, in a very fundamental way, also an American success, albeit a not entirely comfortable one for America. This perhaps adds in no small part to the complexity of the strategic adjustments that are under way between the US and China. But whether it admits it or not, the US too has begun to adapt. There can be no "Clash of Civilisations" because we are now all hybrids.

The inevitably irregular rhythms of economic growth ought to make us cautious about accepting simplistic characterisations of US-China relations as some variant of a contrast between a rising China and a declining US. This posits a false dichotomy. China is certainly rising but the US is not in decline. All who have underestimated American creativity and resilience have come to regret it. The changes in the distribution of power are relative, not absolute. The US is still pre-eminent in most indices of power and is likely to remain so for the foreseeable future.

This is most obvious in the military realm. Before too long, China will reach a more symmetrical military equation with the US in East Asia. This will have very important implications for the maritime disputes in the South China Sea. While military planners cannot ignore any contingency, war is not a very probable scenario. Neither the US nor China is looking for trouble or spoiling for a fight. The essential priorities of both are internal, not external. The most vital of all Chinese interests is the preservation of Chinese Communist Party (CCP) rule. Chinese leaders sometimes talk tough. But they are not reckless.

As the sole global power, the US cannot retreat into complete isolationism. Like it or not, the world will intrude and in East Asia specifically, there has been a fundamental consistency in US policy over the last 40 years or more that I expect will be maintained.

But the political mood that has sustained contenders Donald Trump and Bernie Sanders in their unlikely presidential campaigns is disillusionment with globalisation and working- and middle-class insecurity about their future in an increasingly unfamiliar and uncertain world. Whoever next occupies the White House will talk and even act tougher. But no American president can ignore the national mood, which is not for more wars of choice.

If war between the US and China is highly improbable, is there or will there be a "new Cold War" between the two? There will almost certainly be tense episodes. But I do not think this is an appropriate metaphor to understand the US-China dynamic.

So where does all this leave us? I do not think it makes the strategic adjustments any easier. But it does imply that the parameters within which the US and China must seek a new accommodation are narrower than what we might have been led to expect by the media or the more sensationalist sort of academic analysis.

While it would be futile for the US to try and contain China, it would be equally futile for Beijing to try to exclude the US from East Asia. The delineation of their respective roles is, in fact, what the groping after a new modus vivendi is all about.

I chose the word "groping" with some care. The outcome of the strategic adjustments under way will not be determined by a deliberate process of negotiation, but by the accumulation of a slew of big and small diplomatic, political, military and economic decisions taken at all levels over a long period, probably decades.

The US and China have had a number of senior-level discussions on the "new type of major power relations" that China has suggested. It has three broad elements. Both sides readily agree that they should try to minimise disagreements and foster habits of cooperation. But the US has been unable to give clear endorsement to the third element that is perhaps the most important element to the Chinese: mutual respect for core interests.

Why? I think the US knows that preservation of CCP rule is the most vital of Chinese core interests and is reluctant to endorse this explicitly as this requires a redefinition of American values, including a de facto abandonment of the idea of the universality of democracy that is apparently too painful to bear.

This is a particularly delicate phase of China's development. Beijing is now embarking on a second and more difficult stage of reform that in essence requires loosening the centre's grip on crucial sectors of the economy while preserving CCP rule. Can it be done? One should certainly hope so because all the alternatives are worse. But no one really knows, including, I think, China's leaders.

At a time when the CCP is grappling with existential questions, it is understandable that leaders should regard American attitudes towards universality and incautious words on Hong Kong or Tibet or Xinjiang or Taiwan or other sensitive issues, with grave suspicion: as ultimately intended to destabilise and delegitimise the CCP; a complication to already- complex problems. But there seems to be great reluctance by the US to confront this core issue.

On their part, Chinese leaders and officials, too, do not seem to understand that their own attitudes can evoke distrust. If a new modus vivendi requires the US to acknowledge that different political systems can have their own legitimacy, it requires China to resist the temptations of triumphalist nationalism.

With communism discredited as an ideology, the CCP is increasingly relying on nationalism to legitimise its rule. China never lost its sense of superiority even when powerless before the West and Japan. Now that China has re-emerged as a major power, this sense of superiority has become the underlying cause of the difficulties in China's relations with many countries.

Does this attitude contaminate US-China relations as well? Perhaps not. Some vague notion of equality seems implicit in the concept that China has proposed to the US of a "new type of major power relations".

A stable modus vivendi can be reached only if all parties are operating within the same frame of reference. Are the US and China doing so? I think they do substantially, but not entirely. And from there springs the complexity and risks of the relationship. Can they be brought within a common framework? That is not yet clear. But I do sometimes wonder whether the eventual answer, if there is one, may not prove more challenging than the question.

• The writer is Ambassador-at-large and policy adviser in the Ministry of Foreign Affairs, and the Institute of Policy Studies' 2015/16 S R Nathan Fellow for the Study of Singapore. This is an abridged version of his second IPS-Nathan Lecture on Thursday.