An alarming assumption is taking hold in some quarters of both Beijing and Washington.

Within a few years, China's economy will overtake America's in size. On a purchasing power basis, it is already on the cusp of doing so. Its armed forces, though still dwarfed by those of the United States, are growing fast in strength; in any war in East Asia, they would have the home advantage. Thus, some people have concluded, rivalry between China and the United States has become inevitable and will be followed by confrontation — even conflict.

Some Western hawks see a China threat wherever they look: China's state-owned businesses stealing a march in Africa; its government covering for autocrats in U.N. votes; its insatiable appetite for resources plundering the environment. Fortunately, there is scant evidence to support the idea of a global, Chinese effort to upend the international order. China's desires have an historical, even emotional, dimension. But in much of the world China seeks to work within existing norms, not to overturn them.

In Africa, its business dealings are transactional and more often led by entrepreneurs than by the state. Elsewhere, a once-reactive diplomacy is growing more sophisticated — and helpful. China is the biggest contributor to peacekeeping missions among the U.N. Security Council's permanent five, and it takes part in anti-piracy patrols off the Horn of Africa. In some areas China is working hard to lessen its environmental footprint, for instance through vast afforestation schemes and clean-coal technologies.

The big exception is in East and Northeast Asia — one of the greatest concentrations of people, dynamism and wealth on Earth. There, both its rhetoric and its actions suggest that China is unhappy with Pax Americana. For centuries China lay at the center of things, the sun around which other Asian kingdoms turned. First, Western ravages in the middle of the 19th century and then China's defeat by Japan at the end of it put paid to Chinese centrality.

China's sense of historical grievance explains a spate of recent belligerence. China has deployed ships and planes to contest Japan's control of islands in the East China Sea, grabbed reefs claimed by the Philippines in the South China Sea and moved an oil rig into Vietnam's claimed exclusive economic zone. All this has created alarm in the region. Some strategists say America can keep the peace only if it stands firm. Others urge the U.S. to share power in Asia.

The U.S. cannot walk away without grave consequences. Since the end of World War II, U.S. security has been the basis of Asian prosperity and an increasingly liberal order. It enabled Japan to rise without alarming its neighbors. Indeed, China's race to modernity could not have happened without it. Even Vietnam is clearer than ever that it wants America's stabilizing, reassuring presence.

Yet, if the liberal order is to survive, it must evolve. Denying the reality of China's growing power would only encourage China to reject the world as it is. By contrast, if China can prosper within the system, it will reinforce it. That is why the U.S. needs to acknowledge one increasingly awkward aspect of its leadership: American advantage is hard-wired into the system in ways that a rising power might justifiably resent.

For a great power to find a new equilibrium with an emerging one is hard — because every adaptation looks like a retreat. Three principles should guide America.

First, it should only make promises that it is prepared to keep. On the one hand, America would be foolish to draw red lines around specks of reef in the South China Sea. On the other, if America is to count for anything, its allies need to know that they can depend on it. Although Taiwan is central to China's sense of its own honor, America should leave Beijing in no doubt that it would come to the island's defense.

Second, even in security, America must make room. China's participation in America's recent RIMPAC naval exercises off Hawaii was a start. China could be invited to join Asian exercises, including for disaster relief.

Lastly, America will find it easier to include China in new projects than to give ground on old ones — and should make more effort to do so. It is nonsensical that America should be leading the formation of the region's biggest free-trade area, the Trans-Pacific Partnership, without the inclusion of the region's largest economy. And there is no reason to exclude China from cooperation in space. Even during the Cold War American and Soviet astronauts worked together.

Why should China be satisfied with a bit more engagement when primacy is what it seeks? There is no guarantee that it will be. Just now the rhetoric coming out of Beijing is full of Cold War, Manichaean imagery. Yet sensible Chinese understand that their country faces constraints — China needs Western markets, its neighbors are unwilling to accept its regional writ and for many more years the United States will be strong enough militarily and diplomatically to block it.

Drawing China into a strengthened regional framework would not be to cede primacy to it. Nor would it be to abandon a liberal order that has served Asia — and America — so well. It may, in the end, not work. But given the huge dangers of rivalry, it is essential now to try.

Copyright 2013 The Economist Newspaper Limited, London. All Rights Reserved. Reprinted with permission.