"China supports the DPRK's continued adherence to the direction of denuclearization on the peninsula, supports the continuous improvement of inter-Korean relations, supports the DPRK and the United States holding summits and achieving results, and supports relevant parties resolving their respective legitimate concerns through dialogue", Xi told Kim during their face-to-face meeting in Beijing, Xinhua reports.
AFP journalists saw the distinctive olive green train with a single yellow stripe leave a station in central Beijing, a day after Mr Kim's arrival on a visit to meet Chinese President Xi Jinping to seek economic support and diplomatic backing from his key ally.
At their first meeting in Singapore in June, Kim and Trump signed a vaguely worded document with Kim pledging to work towards the "denuclearization of the Korean peninsula".
Progress has been slow ever since as the North wants sanctions relief, while the USA remains firm that sanctions will remain in place until the North completely gives up its nuclear weapons program.
Mr Xi said China supported North Korea and the USA "holding summits and achieving results, and supports relevant parties resolving their respective legitimate concerns through dialogue".
He "spoke highly of the positive measures taken by the DPRK side", it added.
Washington asserts Kim accepted the "final, fully verified denuclearization of North Korea", while Pyongyang says the deal implied a step-by-step approach where its actions were simultaneously met by US responses.
Kim has previously said his country has completed the development of its nuclear arsenal and Pyongyang has rejected demands for what it calls its "unilateral" disarmament as "gangster-like".
Mr Kim had said in his annual new year's speech in January that he remained committed to denuclearisation, but warned that he would change course if U.S. sanctions remained.
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It said the Chinese leader had issued a ringing endorsement of the North's position.
His trip to China, the fourth in the past 10 months, is believed to be an effort to coordinate with his only major ally ahead of a possible second meeting with Trump. China also wants the sanctions to be relaxed.
South Korean President Moon Jae-in has said North Korea should take bold steps towards denuclearisation, such as abandoning long-range missiles, to extract United States concessions amid a prolonged stalemate in their nuclear negotiations.
In a New Year speech, Kim warned that Pyongyang may change its approach to nuclear talks if Washington persists with sanctions.
The visit coincides with negotiations between United States and Chinese officials in Beijing to resolve a bruising trade war between the world's two biggest economies.
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.
The comments, contained in reports Thursday from Chinese and North Korean state media, came a day after Kim left Beijing on his special armoured train for Pyongyang after a two-day visit to the Chinese capital.
Kim emerged from his quarters around 4 p.m.to meet with Chinese President Xi Jinping at the Great Hall of the People, where Kim's wife Ri Sol-ju joined them later.
Mr. Kim could not be seen, but he was presumed to be on board the long train as it crossed on elevated tracks over a busy Beijing street and headed toward eastern China and the border with North Korea.