On whether Kim's Beijing visit was related to a second North Korea-U.S. summit, Lu Kang, spokesman of the Chinese Foreign Ministry, said in a briefing Tuesday, "China maintains that it is very useful for the DPRK and the U.S.as key parties to the Korean Peninsula nuclear issue to maintain contacts". He said Beijing remains supportive of efforts to end tensions over US demands for a halt to North Korea's nuclear and missile programs.
China is the North's sole major ally and key trade partner but relations had deteriorated over Pyongyang's nuclear activities, before warming up past year, with Kim meeting Xi three times.
Mr Moon said Kim's Beijing visit was a "sign" that a second face-to-face meeting with Mr Trump may be imminent.
Pyongyang needed to take "bold, practical measures for denuclearisation" to ensure sanctions are lifted, he told reporters, but added that "corresponding measures" were also needed from the USA, such as agreeing a "peace regime" and formally declaring an end to the 1950-53 Korean War.
Kim, for his part, welcomed China's readiness to "jointly study and steer" the situation to help ease tensions, as well as the positive role Beijing continues to play in the negotiations process, KCNA said.
Xi told Kim that that China supports the U.S. His delegation was seen off by high-ranking Chinese officials and honour guard at a Beijing train station and could return to North Korea as soon as Thursday morning, Yonhap said.
According to the official readout by China's Xinhua News Agency of Kim and Xi's meeting this week in Beijing, Xi "supported [North Korea] and the United States holding summits and achieving results".
Kim also said North Korea hopes its "legitimate concerns" will be given due respect, a reference to its desire for security guarantees and a possible peace treaty to formally end the 1950-53 Korean War.
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The US insists that United Nations sanctions must remain in place until North Korea gives up its weapons, while Pyongyang wants them immediately eased.
South Korea's President Moon Jae-in urged North Korea to take firmer disarmament measures and the U.S.to reward them, suggesting Thursday he'll push for sanction exemptions to restart dormant economic cooperation projects with the North.
Kim agreed to visit Seoul during the third inter-Korean summit held in Pyongyang in September.
Xi greeted Kim at Beijing's ornate Great Hall of the People on Tuesday - believed to be the North Korean leader's birthday - before hosting a welcome banquet for Kim and his wife Ri Sol Ju.
Kim Jong-un visits a Tong Ren Tang pharmaceutical plant in Yizhuang, Beijing on Wednesday.
Kim previously met with Xi before and after the Singapore Summit with Trump.
"To resolve the issue of global sanctions on North Korea, I believe the North should take practical, bolder steps towards denuclearization".
It comes after US and North Korean officials are thought to have met in Vietnam to discuss the site of the summit.
However, a meeting between Mr Pompeo and senior North Korean official Kim Yong Chol has yet to be rescheduled after an abrupt cancellation in November. However, after the June summit, progress between North Korea and the USA stalled over fundamental disagreements on their respective definitions of "denuclearization" and a timeline for said denuclearization.