“We’re not seeking – say it again, we are not seeking – a new cold war or a world divided into rigid blocs,” President Joe Biden told the United Nations general assembly on Tuesday. That is a relief. Washington’s undeclared opponent is, as almost all observers agree, Beijing. In his address, however, Mr Biden made it clear he is determined to ensure that the rise of China will not mean the decline of the US.

The US president said he was willing to “work together with our democratic partners” on breakthroughs in technology which can be “used to lift people up … and advance human freedom – not to suppress dissent or target minority communities”. This is admirable rhetoric, though some sceptics may spy the promotion of US national interests under the guise of a foreign policy that favours democracies. There are also dangers in an overly hawkish prosecution of this approach. Pushing Ukraine’s membership in Nato as a pro-democracy step may bring about a Russian military response. Taiwan’s democracy has to be defended without Washington being pulled into a confrontation with Beijing. The challenges of this era, such as the climate emergency, also require international cooperation to deliver global public goods and prevent beggar-thy-neighbour policies.

The problem is twofold. First, Mr Biden seems to see US rivalry with China as a zero-sum game, where one country’s gain is another country’s loss. Second, China’s president, Xi Jinping, has the same view of the US. This has the potential for competition between the two powers to spiral out of control. Mr Biden talks of carefully managing relationships so that they do not tip “from responsible competition to conflict”.

His policy is a world away from the cold war strategy of “containment”. But the risks are real. Cooperation is needed to balance competition in world affairs, otherwise nationalism will become even more of a driving force in international affairs.

That might explain why Mr Biden had no time for a US-UK trade deal, which would only feed Boris Johnson’s delusions. Brexiters may seek solace in the argument that Mr Biden is anti-free trade, but that neglects his support for a new US-Mexico-Canada deal that included worker and environmental protections. Claiming Britain could sign up to this free trade pact is gathering Brexit crumbs from the US table.

New forms of cooperation and coordination are needed in the international arena. Britain’s search for a trade pact that could replace the EU’s market may prove fruitless, but that the country is looking for one underlines what it has lost. Mr Biden, whose formative political years were spent with Kremlin officials on arms control, knows that multilateralism requires working with nations irrespective of their system of government. There can be no reduction in nuclear weapons without deals with autocrats.

Mr Biden withdrawal of US troops from Afghanistan crystallised two questions: what is the future of US alliances, and what should be done about China? The time for foreign policy crusades is over but the fight goes on against poverty, the pandemic and global heating. With a majority of American voters now favouring diplomacy over military intervention, the US president ought to embrace collective action rather than go-it-alone policies.