The presidents of China and the United States left the door ajar, if not wide open, for cooperation rather than confrontation on global issues in major speeches to world leaders at the United Nations General Assembly. It was the least they could do in response to UN Secretary General Antonio Guterres’ plea ahead of the meeting to repair their “dysfunctional” relationship to avoid a new cold war. Each pledged to help press the fight against the Covid-19 pandemic and global warming , even as they offered different visions of world order. In a pre-recorded speech delivered by video link, President Xi Jinping said: “Differences in problems among countries need to be handled through dialogue and cooperation.” He highlighted the need for inclusive growth, mutual solidarity and better global governance based on equality. To that end he proposed a six-point Global Development Initiative to revitalise the economy and pursue more robust, greener and more balanced development, which requires detailed action plans for implementation. US President Joe Biden , in his first address to the assembly, emphasised the need for rules-based systems to manage increasingly complex global trade and technology networks. “We are not seeking a new cold war or a world divided into rigid blocs. The United States is ready to work with any nation that steps up and pursues peaceful resolution to shared challenges.” The world’s two largest carbon emitters reaffirmed their commitment to fight global warming and both leaders promised greater support for global vaccine programmes. These are all encouraging words but, generally, the world has reason to remain sceptical. The US may say it has no intention to start a new cold war, but it has just formed a military alliance with Australia and the United Kingdom, called Aukus, which is not only clearly targeting China but also dividing Asian countries. Indeed, few in the region feel at ease with the new alliance. Biden may disavow any intention to create blocs, but the one he has just created causes confusion. Many countries want to find out more about China’s future role in vaccine distribution to developing countries and in fighting climate change . Likewise with Xi’s assurance that China has never and will never invade or bully others, or seek hegemony. Members of the Association of Southeast Asian Nations in particular want more concrete reassurance amid competing claims in the South China Sea. It is good for a superpower and a rising rival to make these promises to the world, but they need to be mindful that they are viewed with a healthy dose of scepticism. This is understandable when the US talks down a new cold war while creating blocs and dividing the region, and while China needs to come up with more detail and concrete action to reassure regional countries.