At a summit with Xi in Beijing on Monday, Kim was quoted by Xinhua News Agency as saying the goal of his visit to China was to "enhance strategic communication and deepen traditional friendship" between the two nations.
Also Thursday, China's top diplomat, State Councillor Yang Jiechi, was due to travel to Seoul to brief Moon on Kim's secretive visit to Beijing this week to meet Chinese President Xi Jinping for the first time.
Since late previous year, China, one of the five permanent U.N. Security Council members, has bolstered economic sanctions against Pyongyang, dealing a severe blow to North Korea's economy, foreign affairs experts said.
Hotham, the Korea Risk Group expert, said Moon has "staked a lot on his more diplomatic approach to the North working".
"Investors seem to be betting on won strength as the so-called "Korea discount" is relatively lifted with tension easing", said Park Jeong-woo, a Seoul-based economist at Korea Investment & Securities, referring to the history of tension between South and North Korea.
"China will not simply look on", it added. "But, it won't be easy because the U.S.is pressuring North Korea strongly to accept Libyan-model solutions by hiring [the hawkish Mike] Pompeo [as Secretary of State] and others, while Pyongyang will try to resist this".
Trump is expected to meet with the North Korean despot before the end of May. But neither country's state-run media reported Song meeting with Kim.
It comes in sharp contrast to 2017 when the peninsula appeared to be barreling toward conflict, with Kim overseeing a string of missile and nuclear tests and Trump promising "fire and fury" as Pyongyang threatened Guam, Hawaii and even the USA mainland.
Thursday's North and South Korean delegations were both headed by the same men who engaged in the first negotiations in January, after Pyongyang agreed to reopen diplomatic communications with Seoul. "North Korea summit will be a very hard one".
Ministers from the two Koreas agreed on Thursday to hold the Moon-Kim summit on April 27 inside the Demilitarized Zone between the two countries. The meeting followed a sudden period of inter-Korean warmth over February's Winter Olympics in the South, to which the North sent hundreds of officials, including Kim's sister who met with Moon to convey her brother's desire for a summit. Since late November, Pyongyang has carried out no new nuclear or ballistic missile tests. The cost of insuring the nation's five-year notes using credit default swaps declined this week.
In setting up separate talks with Beijing, Seoul, Washington, and potentially with Moscow and Tokyo, North Korea may be moving to disrupt any united front among its negotiating counterparts.
Mr Kim is also scheduled to meet US President Donald Trump some time in May to discuss denuclearisation, although a time and place have not been set for that summit. Seoul and Pyongyang will continue exchanging documents as they prepare.
"North Korea and the USA have big differences in how to resolve the denuclearization issue".
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