Biden was expected to press Xi to use his leverage over Kim Jong Un to dissuade North Korea from further deepening its support for Russia's war in Ukraine but there were no reports any such talks took place.
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Joe Biden has met China's President Xi Jinping for the final time before he leaves the White House in January and hands the presidency back to Donald Trump.
Xi was already looking ahead to Trump’s return and his 'America First' policies, saying Beijing "is ready to work with a new US administration."
During their talks on the sidelines of the annual Asia-Pacific Economic Cooperation (APEC) summit in Peru, Xi cautioned that a stable China-US relationship was critical not only to both countries but also the "future and destiny of humanity."
"Make the wise choice,” he warned. "Keep exploring the right way for two major countries to get along well with each other."
Without mentioning Trump by name, Xi appeared to signal his concern that the incoming president's protectionist rhetoric on the campaign trail could spark another low point in the US-China relationship.
Biden, who is winding down more than 50 years of public service, talked in broader brushstrokes about where the relationship between the two countries has gone.
He reflected not just on the past four years but on the decades the two leaders have known each other.
"We haven't always agreed, but our conversations have always been candid and always been frank. We've never kidded one another," Biden said.
"These conversations prevent miscalculations and they ensure the competition between our two countries will not veer into conflict."
Biden was expected to press Xi to use his leverage over Kim Jong Un to dissuade North Korea from further deepening its support for Russia’s war in Ukraine but there were no reports any such conversation took place.
On Friday, Biden, South Korean President Yoon Seok Yul and Japanese Prime Minister Shigeru Ishiba condemned Kim's decision to send thousands of troops to help Moscow repel Ukrainian forces who have seized territory in Russia's Kursk border region.
Biden called it "dangerous and destabilising cooperation."
White House officials have expressed frustration with Beijing, which accounts for the vast majority of North Korea's trade, for not doing more to rein in Pyongyang.
The North Koreans also have provided Russia with artillery and other munitions, according to US and South Korean intelligence officials.
An uncertain future
There's some uncertainty about how the US-China relationship will look under the Trump presidency, who campaigned promising to levy 60% tariffs on Chinese imports.
In a congratulatory message to Trump after his victory over Vice President Kamala Harris, Xi called for Washington and Beijing to manage their differences and get along in a new era.
In front of the cameras Saturday, Xi may have been speaking to Biden but many interpreted his words as being directed at Trump.
"In a major flourishing sci-tech revolution, neither decoupling nor supply chain disruption is a solution," Xi said.
"Only mutual, beneficial cooperation can lead to common development. 'Small yard, high fence' is not what a major country should pursue."
Biden administration officials would advise the Trump team that managing the intense competition with Beijing will likely be the most significant foreign policy challenge they will face, White House national security adviser Jake Sullivan said.
Biden has viewed his relationship with Xi as among the most consequential on the international stage and put much effort into cultivating it.
"For over a decade, you and I have spent many hours together, both here and in China and in between," Biden said.
"We've spent a long time dealing with these issues."