South Korean President Moon Jae-in made the statement during the ASEAN-South Korea summit in Manila, one in a long series of meetings between the regional bloc and its dialogue partners.
Premier Li responded saying he saw a "bright" future for their bilateral relations, according to South Korea's Presidential website.
During Saturday's summit, Moon and Xi also agreed to quickly normalise bilateral exchanges in all sectors, Yoon added, repeating what was said in the agreement announced last month when the two countries agreed to end a year-long standoff over the deployment of a US anti-missile system.
Xi said China was willing to work with South Korea to improve bilateral ties, but called on Seoul to make responsible decisions about THAAD.
Moon, who sent a special envoy to the Association of Southeast Asian Nations (ASEAN) after his inauguration this year, promised to strengthen relations with the bloc "to the highest level".
Abe also said China and Japan agreed to deepen cooperation on Pyongyang, and hailed a "fresh start" to ties between Beijing and Tokyo.
"During the APEC summit on Saturday, Moon and Xi also agreed to immediately normalize bilateral exchanges in all sectors", Yoon added.
Better relations with China will help the nation withstand potential rough economic conditions next year, South Korean Vice Finance Minister Ko Hyoung-kwon told Bloomberg News in an interview last week.
South Korea's foreign minister is expected to visit China soon to fine-tune preparations for the upcoming summit between their leaders, a government source said Monday.
Officials are seeking to resume an annual summit between China, Japan and South Korea, which was scheduled for July but postponed as Beijing and Tokyo locked horns over maritime sovereignty in the East China Sea, and China and South Korea squabbled over THAAD.