How many ways are there to say you’re back? In 2010, Hillary Clinton grabbed Beijing’s lapels when she declared the South China Sea, claimed in its entirety by China, was also a vital American interest. A few weeks ago, the secretary of state published a lengthy piece in Foreign Policy magazine in which she laid out the terms of what she called America’s Pacific Century. And this week, at the Asia-Pacific Economic Co-operation forum in Honolulu, Barack Obama talked about hardly anything else. “The US is a Pacific power and we’re here to stay,” he said. The message is clear. America is back. And by the way, it never left.

In her essay, Mrs Clinton elaborates on what kind of engagement she favours. “We must create a rules-based order – one that is open, free, transparent and fair.” America, she says, is uniquely placed to create such an order and to police it. “We are the only power with a network of strong alliances in the region, no territorial ambitions, and a long record of providing for the common good.”

The words are about the future. But they hark back to the past. It will not be so easy to reinvent a time when, after the war, the US had no credible rival for the role of honest broker. Japan had been defeated and turned into the US’s unsinkable aircraft carrier. China was poor and consumed by its own Maoist revolution.

Today China has stirred from its slumbers. The US now has a significant rival, if not yet globally, then certainly in Asia. As Lee Hsien Loong, Singapore’s prime minister, puts it, Asia is just one region for the US. China is here all the time.

This week, two elements of Washington’s strategy came together. Mr Obama launched the Trans-Pacific Partnership, a so-called 21st century trade pact meant to incorporate non-tariff issues, such as intellectual property protection and state procurement.

Trade officials have talked up the TPP’s “next-generation” qualities. But the most glaring thing about it is that it does not include China, Asia’s biggest trading nation. That could be, as US officials say, because China – with its state-owned enterprises, piratical tendencies and questionable currency policy – is not yet ready to join such a high-level agreement. Yet Vietnam, hardly a paragon of free-market capitalism, is one of nine negotiating countries.

Beijing might be forgiven for thinking that TPP looks like a club to which it has not been invited. It is one element of the rules-based order Mrs Clinton talked about. The rules are made in America. In the long run, in keeping with Robert Zoellick’s notion of making China “a responsible stakeholder”, the idea may be to lure China into abiding by a higher code than the World Trade Organisation can enforce.

The second element is security. Mr Obama said in Hawaii this week that planned cuts to the US defence budget would not affect the US’s presence in Asia. On Tuesday, he was in Darwin to visit new facilities that will house a semi-permanent Marine presence in Australia.

Put the TPP and stronger bilateral military ties together and you have something approaching the vision of Kevin Rudd, Australia’s foreign minister and former prime minister. Mr Rudd was constantly searching for ways of binding the US more firmly into Asia’s still-developing institutional architecture. Countries nervous about China’s rise – such as Vietnam, the Philippines and even Singapore – quietly welcome these signs of revived US commitment.

But there are forces pulling in the opposite direction. As China’s clout grows, it seems almost perverse that the US would embed itself more deeply into the region. Asians have grown accustomed to the US presence. But one only has to imagine a Chinese aircraft carrier sailing merrily past San Francisco to realise that there is nothing inevitable about the US – Pacific power or not – being engaged so deeply in Asian territory.

A minority in the US argues that Washington should read the writing on the Great Wall and begin to draw down its presence. Clyde Prestowitz, president of the Washington-based Economic Strategy Institute, is one. He says America spends too much time worrying about grand strategic goals and not enough about making its economy strong.

One participant at the Apec summit this week tried to square the circle. Susilo Bambang Yudhoyono, president of Indonesia, said that, while he welcomed the US presence, it was no longer desirable for the region to be dominated by a sole superpower. “New power centres are growing rapidly and power relationships are changing and becoming fluid,” he said.

It was the task of all interested nations to make sure this new state of affairs did not spill over into tension – or worse. He proposed establishing a “dynamic equilibrium”. It is a difficult concept. But what he probably meant was that this should not be an American Pacific Century, nor a Chinese one. It may be a fantasy, but Mr Yudhoyono wants a Pacific century that belongs to everyone.