Separately China Central Television (CCTV) reported that Xi had told South Korean Prime Minister Han Duck-soo on Saturday that China is willing to work to promote a strategic partnership between the two countries.
Xi, who has not visited South Korea since 2014, held talks with Han in the eastern Chinese city of Hangzhou before the opening ceremony of the Asian Games on Saturday.
The commitment to cooperation came ahead of scheduled trilateral talks in Seoul on Sept. 26 involving senior officials from China, Japan and South Korea, intended to pave the way for the first summit between the three countries in four years.
Xi told Han he would welcome such a summit at an opportune time and would seriously consider visiting South Korea, Yonhap reported.
A Chinese statement did not mention Xi's comment on the summit or a visit to Seoul.
China attaches great importance to the positive willingness of South Korea to commit to cooperation, Xi said, according to CCTV, and asked South Korea to meet it half way to maintain the direction of friendly cooperation. The two countries can deepen mutually beneficial cooperations, he said.
Citing what it said was a high-ranking South Korean government official, Yonhap reported that Xi had said China supports dialogue between the two Koreas and will continue efforts for peace and security on the Korean Peninsula, while Han had asked China to play a constructive role in relations with North Korea.
Tensions between the two countries rose after North Korea's Kim Jong Un made a week-long visit to Russia earlier this month, which angered the United States, Japan and South Korea.
South Korea imposed sanctions on 10 individuals and two entities in relation to North Korea's nuclear program and weapons trade with three countries, including Russia, the foreign ministry said on Thursday.
(Reporting by Albee Zhang and Ryan Woo in Beijing and Joyce Lee in Seoul; Editing by Mike Harrison and David Holmes)
