Discussions between the U.S. and North Korea over Pyongyang's nuclear arsenal have stalled since Kim and Trump's high-profile summit in Singapore in June where they issued a vaguely worded declaration about denuclearisation.
But progress has since stalled with Pyongyang and Washington - which stations 28,500 troops in South Korea - disagreeing over what that means.
The US insists that United Nations sanctions must remain in place until North Korea gives up its weapons, while Pyongyang wants them eased immediately. The North Korean leader confirmed he remains committed to the consensus reached during the Singapore summit with Donald Trump previous year.
Details of his visit weren't released, but Yonhap said Kim met with Chinese President Xi Jinping.
Pyongyang has rejected demands for what it calls its "unilateral" disarmament as "gangster-like".
Mr Kim arrived in Beijing on Tuesday for a fourth visit to his country's sole major diplomatic friend, a trip seen as a strategy session ahead of his possible second meeting with Mr Trump on Pyongyang's nuclear programme.
Kim and his delegation are now expected to begin the 13-hour trip to the town of Dandong, which sits on the border between China and North Korea.Kim is expected to spend a total of four days in China, entering the country Monday and leaving early on Thursday.
Mr Kim renewed his resolve to meet Mr Trump again during his meeting with Chinese President Xi Jinping in Beijing this week.
At Tuesday's daily Foreign Ministry briefing, spokesman Lu Kang said Beijing remains supportive of efforts to end tensions over USA demands for a halt to North Korea's nuclear and missile programs.
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ABC News also reported that there is no indication that Trump is attempting to force out Rosenstein, despite their rocky past. If confirmed, Barr would be in charge of Mueller, unless he too recused himself.
Thus, it's highly likely Kim has pledged to continue exchanges with China in various sectors outside the framework of worldwide sanctions, . while intensifying strategic solidarity with his Chinese counterpart to push the U.S.to offer some form of sanctions relief.
Moon acknowledged the Singapore agreement was "somewhat vague", and there was "scepticism" over Kim's denuclearisation pledge.
"I expect we'll hear about high-level talks between North Korea and the United States before long for their second summit", he added.
Nonetheless a commentary carried by KCNA last month stressed that when Pyongyang refers to "denuclearisation of the Korean peninsula", it includes the North, the South, and "surrounding areas from where the Korean peninsula is targeted".
Experts say Beijing has an interest in establishing a peace regime on the Korean Peninsula and adapting to the changing diplomatic landscape in Northeast Asia.
Beijing stands ready to "play a positive and constructive role in maintaining peace and stability and realising denuclearisation on the peninsula and lasting peace and stability in the region", it cited him as saying.
A auto carrying North Korean leader Kim Jong-un heads to the Diaoyutai State Guesthouse in Beijing on Tuesday.
Kim Jong-un visits a Tong Ren Tang pharmaceutical plant in Yizhuang, Beijing on Wednesday.
Kim's visit coincided with negotiations between U.S. and Chinese officials in Beijing to resolve a bruising trade dispute between the world's two largest economies that has roiled financial markets.
Kim could not be seen but the limousine he uses was observed zipping east down a main thoroughfare in Beijing and then returning about an hour later.