Mr Moon said North Korea should take more concrete steps, such as abandoning its intercontinental and intermediate-range ballistic missiles and dismantling weapons production lines and other nuclear complexes, to secure U.S. concessions such as sanctions relief.
Kim's grandfather Kim Il Sung was also adept at playing off Communist rivals Beijing and Moscow against each other during the Cold War to extract concessions from both.
Pyongyang could be using the visit to show the United States that it has an "alternative power to gravitate towards", according to Tai Wei Lim, a research fellow at the National University of Singapore. Video footage shown on South Korean and Japanese media showed streets being cleared of traffic for a convoy of luxury vehicles, supposedly shuttling Kim through Beijing. While there have been reports of easier inspections at the North Korean border, China has denied that it's relaxing pressure on the regime. The two sides are wrangling to draft a deal before March 2, when United States tariffs on Chinese goods are expected to intensify if no agreement is reached. -China negotiations were extended another day to Wednesday.
"The second summit would be a venue where they settle on terms of what specific measures North Korea will take and how those moves will be reciprocated by the United States", Mr Moon told a news conference at the presidential Blue House in Seoul.
"China stands ready to work with the DPRK and relevant parties to play a positive and constructive role in maintaining peace and stability and realizing denuclearization on the peninsula and lasting peace and stability in the region". But others say Moon simply made a symbolic, conciliatory gesture toward North Korea.
The Global Times wrote, "The second summit is so important that Kim feels it is necessary to break protocol and consult Chinese leaders before shaking hands with Trump once again".
"Xi Jinping said that the legitimate issues raised by the DPRK are rightful demands and that he fully agrees that the DPRK's reasonable interests should be justly resolved", it said, using the official country name the Democratic People's Republic of Korea. The factory is run by Tong Ren Tang, the country's largest producer of traditional Oriental medicine.
But so far Kim's strength has been in what he doesn't say.
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We can safely assume that Kim Jong-un has known all along that America wouldn't be abandoning their own nuclear weapons arsenal or unilaterally pulling all of our troops out of South Korea.
While Trump is happy to broadcast his plans and successes on Twitter, Kim's skill as a negotiator lies in not showing his cards "until the very last moment", added Kim.
"If Washington will not give him (Kim) economic concessions, China in a subtle way nearly certainly will. albeit with the expectation he does make progress and does not return to belligerence".
In fact, according to Klingner, any steps North Korea is taking appear to be in the wrong direction.
Trump, in turn, has sometimes blamed China for impeding denuclearization talks with North Korea.
The trip also came after he expressed frustration in his annual New Year's address over the lack of progress in negotiations with Washington since the Singapore summit, saying that if things don't improve - meaning that if sanctions relief and security guarantees aren't in the offing - Pyongyang might have to find "a new way" forward.
"But Kim has assured many foreign leaders, including myself, Trump, Xi Jinping and Putin, that his concept is no different in any way from what the worldwide community demands", Moon told reporters at the Blue House in Seoul.