Biden and Xi met on the sidelines of the Asia-Pacific Economic Cooperation (APEC) summit in Peru, two months before Trump takes office and amid concerns of new trade wars and diplomatic upheaval.
China claims Taiwan as its own territory and has refused to rule out using force to seize it, while the United States is the self-ruled island's main security backer even though it does not recognise Taipei diplomatically.
Xi told Biden that the "Taiwan issue, democracy and human rights, pathways and systems, and development interests are China's four red lines that must not be challenged", according to Chinese state broadcaster CCTV.
"These are the most important guardrails and safety net for China-US relations," CCTV reported Xi as saying.
"The separatist actions of 'Taiwan independence' are incompatible with peace and stability in the Taiwan Strait," he added.
Taiwan's foreign ministry said Sunday that "China's ongoing military provocations near Taiwan are the root cause of destroying regional peace and stability and the major threat to global economic prosperity".
Xi also told Biden that Washington "should not intervene in bilateral disputes... and not condone or support provocative impulses" in the South China Sea, according to CCTV.
Beijing has this year pressed its sweeping claims in the contested waterway with greater assertiveness, despite increased frictions with regional neighbours and a longstanding international ruling that its claims have no legal basis.
Xi also said China's position on the war in Ukraine was "open and aboveboard", and that Beijing would not allow tensions on the Korean peninsula to "descend into conflict or chaos", CCTV reported.
He announced during a separate meeting that China would host the next APEC summit in 2026.
State news agency Xinhua said those talks would aim to "unite Asia-Pacific countries to champion open economic and trade cooperation while rejecting protectionist and confrontational trade tactics".
- 'Smooth transition' -
But Xi said China would "strive for a smooth transition" in relations with the United States and is ready to work with the incoming Trump government.
"China is ready to work with the new US administration to maintain communication, expand cooperation and manage differences, so as to strive for a smooth transition of the China-US relationship," Xi told Biden through a translator.
In his first White House term, Trump engaged in a bruising trade war with China, imposing tariffs on billions of dollars in Chinese products and drawing retaliation from Beijing.
He embraced a similar stance on the campaign trail this year.
Both sides should "keep exploring the right way for the two major countries to get along well with each other," Xi said.
Xi warned Saturday that bilateral ties could "encounter twists and turns or even regress" if one side regarded the other as an opponent or enemy, according to the official Xinhua news agency.
"Major country competition should not be the underlying logic of the times," Xi added, urging against a "small yard, high fences" approach.
He added that "a stable China-US relationship is critical" to both parties and the world, noting that Beijing continues to aim for healthy ties.
But he stressed that Beijing's position of "firmly safeguarding its sovereignty, security and development interests has not changed," according to Xinhua.
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