The men, who will hold their last, official face-to-face Saturday, warned separately of choppy waters as the world braces for the prospect of fresh trade wars after Trump assumes the presidency in January.
Xi raised concerns about “spreading unilateralism and protectionism”, China’s state news agency Xinhua reported.
He also cautioned against “fragmentation of the world economy” in a written speech prepared for a meeting of CEOs on the sidelines of the Asia-Pacific Economic Cooperation (Apec) summit, Xinhua said.
Biden, for his part, said the world had “reached a moment of significant political change”, as he met the leaders of Japan and South Korea – key US allies in Asia.
The trilateral partnership, Biden said, was “built to last. That’s my hope and expectation.”
Xi and Biden are in the Peruvian capital for a two-day meeting of heads of state of the 21-member Apec group.
They separately met on Friday with South Korean president Yoon Suk-yeol, who called for co-operation for the sake of “stability and peace in the region,” according to the Yonhap news agency.
China is an ally of North Korea, with which Seoul remains technically at war and whose leader Kim Jong-un has engaged in escalatory rhetoric and military posturing this year.
Biden, for his part, warned of North Korea’s “dangerous and destabilising cooperation with Russia” amid growing concerns about nuclear-armed Pyongyang sending troops to fight in Ukraine.
‘Delicate period of transition’
Apec, created in 1989 with the goal of regional trade liberalisation, represents about 60% of world GDP and more than 40% of global commerce.
The 2024 summit programme was to focus on trade and investment for what proponents dubbed inclusive growth.
However, uncertainty over Trump’s next moves clouds the agenda – as it does for the COP29 climate talks underway in Azerbaijan, and a G20 summit in Rio de Janeiro next week.
The Republican president-elect has signalled a confrontational approach to Beijing for his second term, threatening to impose tariffs of up to 60% on imports of Chinese goods to even out what he says is a trade imbalance.
Xi was not present for Friday’s summit opening, but Biden attended with US secretary of state Antony Blinken – whom Trump has said he will seek to replace with Senator Marco Rubio, a China hawk.
US national security adviser Jake Sullivan said Saturday’s Xi-Biden meeting will be an opportunity to “mark the progress that we’ve made in the relationship and also to manage it through this delicate period of transition.”
Competition with China, he told reporters on Air Force One Thursday, must be managed “so it doesn’t veer into conflict”.
‘America first’
Trump’s “America first” agenda is based on protectionist trade policies, increased domestic fossil fuel extraction and avoiding foreign conflicts.
It threatens alliances Biden has built on issues ranging from the wars in Ukraine and the Middle East to climate change and trade.
Economists say Trump’s threat of punitive tariffs would harm not only China’s economy but also that of the US and its trading partners.
It could also threaten geopolitical stability.
China is building up its military capacity while ramping up pressure on self-governed Taiwan, which it claims as part of its territory.
China isn’t the only Apec economy in Trump’s crosshairs.
The incoming US leader has threatened tariffs of 25% or more on goods coming from Mexico unless it stops an “onslaught of criminals and drugs” crossing the border.
The Apec summit is also attended by Chile, Canada, Australia and Indonesia, among others.
Russia is additionally part of Apec but president Vladimir Putin was absent.