China is a key ally of North Korea, with whom Seoul remains technically at war and whose leader Kim Jong Un has engaged in escalatory rhetoric and military posturing this year.
"I hope that our two nations will cooperate to promote stability and peace in the region in response to North Korea's repeated provocations, the war in Ukraine and military cooperation between Russia and North Korea," Yonhap quoted Yoon as saying.
The two leaders met on the sidelines of the Asia-Pacific Economic Cooperation (APEC) summit in Peru, which brings together 21 economies that jointly represent about 60 percent of world GDP.
Yoon's government has repeatedly expressed concern at deepening military cooperation between Pyongyang and Moscow, including the deployment of North Korean troops to take part in Russia's war in Ukraine.
The Chinese state media readout of the meeting made no mention of North Korea or Russia.
Xi "called on China and South Korea to promote a sound and steady development of the strategic cooperative partnership between the two countries," Chinese state news agency Xinhua reported.
Beijing and Seoul are major trading partners, despite China being North Korea's main diplomatic and economic backer, and the South being militarily allied with the United States.
China has called in the past for a "political settlement" to resolve tensions on the Korean peninsula, reiterating that position after the North declared Seoul a "hostile" state earlier this year.
China's relationship with South Korea is not without its difficulties. Last month, Beijing said it had detained a South Korean citizen for alleged spying.
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