Kim visited Beijing by train this week for two days of talks that reasserted China's role in the process, and were seen as a strategy session ahead of a second summit between the North Korean leader and US President Donald Trump.
Mr Moon also said the North would have to seek a compromise in a second summit between North Korean leader Kim Jong-un and US President Donald Trump, which he said could be imminent, in order to resolve the impasse.
"The second North Korea-United States summit - to take place soon - and a reciprocal visit to Seoul by Chairman Kim Jong Un of North Korea will be other turning points that will firmly solidify peace on the Korean Peninsula", Moon said Thursday, at his annual press conference.
Moon said resolving the issue of the North Korea sanctions hinges on how fast North Korea denuclearizes and whether it receives reciprocal measures from the United States.
He added that the two-day trip shows that Kim is "sensitive" to the demands of China, North Korea's primary trade and aid source.
"We will not loosen our guard until the promise to denuclearize the peninsula is kept and peace is fully institutionalized", Moon said.
He also credited President Xi Jinping with helping reduce regional tensions, saying "the Korean Peninsula situation has been easing since a year ago, and China's important role in this process is obvious to all".
Xi was quoted as saying that China supports the U.S.
The president said he hopes denuclearization will be sped up by the declaration of an official end to the Korean War.
Xinhua quoted Mr Xi as saying he hoped that North Korea and the United States could meet each other half way and that the worldwide community expected peaceful negotiations.
As Pyongyang's only major ally, Kim is hoping Xi can push for relief from the multiple sets of sanctions imposed on it over its weapons programmes.
The North Korean leader visited China at Xi's invitation for the fourth time in less than a year.
While North Korea hasn't conducted any launches or detonations in more than a year, it's displayed no real intention of abandoning the programs that are seen as guaranteeing the government's survival.
Seven months after Trump shook hands with Kim, the US and North Korea continue to argue over what the leaders agreed to do.
It has become something of a ritual: Last year, Kim briefed Xi before and after his historic summits with Trump and South Korean President Moon Jae-in.
Kim "raised concern" about the impasse in talks with the U.S., according to Pyongyang's official KCNA news agency, which said the Chinese leader had issued a ringing endorsement of the North's position.
In this undated image from video distributed on Tuesday, Jan. 1, 2019, by North Korean broadcaster KRT, North Korean leader Kim Jong Un delivers a speech.
Kim previously met with Xi before and after the Singapore Summit with Trump.
"North Korea is looking for something where. they would be rewarded for meeting certain goals, rather than sanctions being lifted only after CVID (complete, verifiable and irreversible destruction) of their nuclear facilities, which is what the United States is adamant on", said Graham Ong-Webb, a research fellow at the S. Rajaratnam School of International Studies in Singapore.
"China has been an important force in promoting the political settlement of the Korean Peninsula nuclear issue and peace and stability on the peninsula", said Lu. Xi then threw a lavish banquet for Kim to celebrate his birthday, but state-run CCTV made no mention of Kim's visit.
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