Lee hosted Xi at a state summit and dinner after an Asia-Pacific leaders' forum in the South Korean city of Gyeongju, marking Xi's first visit to the country in 11 years.
China attaches great importance to relations with South Korea and views it as an inseparable co-operative partner, Xi said ahead of the summit according to Lee's office.
Lee, who was elected president in a snap election in June, has promised to strengthen ties with the United States while not antagonising China and seeking to reduce tensions with the North.
"I am very positive about the situation in which conditions for engagement with North Korea are being formed," Lee said, referring to recent high-level exchanges between China and North Korea.
"I also hope that South Korea and China will take advantage of these favourable conditions to strengthen strategic communication to resume dialogue with North Korea."
Lee has called for a phased approach to denuclearising North Korea, starting with engagement and a freeze on further development of nuclear weapons.
In a statement on Saturday, North Korea dismissed the denuclearisation agenda as an unrealisable "pipe dream".
North Korea has repeatedly and explicitly rejected Lee's overtures, saying it will never talk to the South.
In recent years the North abandoned its longstanding policy of unification with the South and called it a main enemy.
Leader Kim Jong-un said he would be willing to talk to the United States if it drops demands for denuclearisation but he did not publicly respond when US President Donald Trump offered talks during his visit to South Korea earlier this week.
Trump and Lee announced a surprise breakthrough in talks to lower US tariffs in return for billions of dollars in investment from South Korea.
The US president then departed before the main APEC leaders' summit.
South Korean national security adviser Wi Sung-lac told a briefing that China expressed its willingness to co-operate for peace and stability on the Korean peninsula but the leaders did not specifically discuss what kind of role China would play.
Both sides also agreed that US-North Korea dialogue was most important, Wi said.
Chinese state media reports on the meeting with Lee made no mention of the North Korea discussions.
According to Xinhua, Xi proposed ways to open a new chapter in relations, including having each country "respect each other's social systems and development paths, accommodate core interests and major concerns, and properly handle differences through friendly consultation".
Xi also called for upholding multilateralism and increasing co-operation in areas such as artificial intelligence, biopharmaceuticals, green industries and aging populations, Xinhua reported.
During Xi's visit, China and South Korea signed seven agreements including a won-yuan currency swap and memorandums of understanding on online crime, businesses that cater to aging populations and innovation among other issues.
