"China has actually been a good partner in our efforts to reduce the risk to the world from North Korea's nuclear capability; I expect they will continue to do so".
A special train believed to be carrying Kim Jong Un departed Beijing on Wednesday after a two-day visit by the North Korean leader to the Chinese capital.
Abe's latest comments come after Kim traveled to China for discussions with Chinese President Xi Jinping on USA sanctions, after which both leaders issued statements supporting a second U.S.
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.
Like Mr Moon, Mr Xi had emphasised the importance of both sides compromising, suggesting the leaders needed to "meet each other halfway" to break the deadlock.
He "spoke highly of the positive measures taken by the DPRK side", it added.
Among those in Kim's entourage were Kim Yong-chol, a key nuclear negotiator with the USA, and North Korea's foreign and defense ministers, Yonhap noted.
Pyongyang has rejected demands for what it calls its "unilateral" disarmament as "gangster-like".
A lead limousine in the motorcade of North Korean leader Kim Jong-un leaves the gate of the Diaoyutai State Guesthouse in Beijing on Wednesday.
North Korean state news agency KCNA has said Mr Kim and Mr Xi held "in-depth, frank discussions" on the Korean peninsula and nuclear issues during his stay in Beijing, his fourth since March 2018.
While Mr. Trump says he considers Mr. Xi key to enticing Mr. Kim into taking concrete steps toward denuclearization, the president's own relationship with his Chinese counterpart has frayed over the U.S.
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Moon acknowledged the Singapore agreement was "somewhat vague", and there was "scepticism" over Kim's denuclearisation pledge.
Chinese Foreign Ministry spokesman Lu Kang only said, "It is very normal for the two parties and two states to maintain friendly exchanges".
Following their meeting in Singapore where Kim and Trump signed a vaguely-worded document pledging work towards the "denuclearisation of the Korean peninsula", progress has stalled, with Pyongyang and Washington unable to agree on what that means.
Washington and Beijing have competing strategic interests in northeast Asia, and Xinhua said Xi had re-asserted China's importance in the diplomatic process.
"We will not loosen our guard until the promise to denuclearize the peninsula is kept and peace is fully institutionalized", Moon said.
The DongA Ilbo newspaper said that Xi hosted Kim at a banquet, which was held on the date believed to be North Korean leader's 35th birthday.
Kim spent around half an hour touring a pharmaceutical factory operated by Tong Ren Tang, the largest producer of traditional Chinese medicinal products.
Kim's visit coincided with trade talks between Chinese and United States officials in Beijing.
Conditions for resuming two key economic projects between North and South Korea - the Kaesong Industrial Complex, where Southern companies used to employ North Korean workers, and Southern tourism to Mount Kumgang in the North "have essentially been met already", he said.
There was a "rare historic opportunity" for a political settlement on the peninsula, Xi said according to Xinhua, and China "supports the DPRK and the United States holding summits and achieving results".