The ruler of the secretive state left Beijing on his special armoured train yesterday after his fourth trip to China in the last 10 months.
But it may also have sent a message to Trump that Pyongyang has other options if rapprochement with Washington fails.
Trump and Kim met in Singapore in June for the first-ever leaders' meeting between their nations, but there has been a standoff ever since, with dueling accusations of bad faith.
But since North Korea's rapprochement with South Korea and the U.S., Kim and Xi have thawed their frosty relationship, as each wants to negotiate with Trump on a key topic: Kim on denuclearization and Xi on trade.
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.
North Korean leader Kim Jong-un was given a lavish welcome in the Chinese capital on Tuesday, which was his birthday.
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And President Moon expressed optimism that this time.
China is the North Korea's sole major ally and key trade partner.
China and Russian Federation, who both wield vetoes on the United Nations Security Council, have called for easing sanctions to reward Kim's move previous year to halt weapons tests and dismantle some testing facilities. And while Beijing hasn't formally claimed to be ignoring enforcement, reports about "pockets of sanctions violations" are growing, he added.
The recent comments shows that Seoul will likely join Pyongyang in pushing for sanctions relief, but the move could strain ties with the U.S. The Trump administration wants to maintain sanctions until North Korea completely denuclearizes.
The US and the North Korea are reportedly working on hammering out the schedule and location of their second summit. China has also banned imports of textiles from the North, while several countries have an embargo on selling them luxury goods.
Trump's withdrawal from the Iran nuclear deal and Libyan leader Moamer Kadhafi's ouster after giving up his own weapons programme are not distant memories. Rumours of thinly disguised coal shipments to South Korea have added to United States frustrations in getting Kim's neighbours to maintain pressure. Emphasizing the "resolute determination of the two countries to jointly advance the political settlement", China, Xi pointed out, is fully committed to fostering a dialogue between the DPRK and the United States.
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Xi seeks an end to the ongoing trade dispute, which is hurting the Chinese economy. -China negotiations were extended another day to Wednesday. -North Korea summits and hopes the two sides "will meet each other halfway".
The motorcade of North Korean leader Kim Jong Un has headed out on the second full day of his visit to China. He said those would top the agenda in an expected second summit between Kim and President Donald Trump.
Meanwhile, Cheong Wa Dae said it hopes Kim's visit to China "lays the groundwork" for a second U.S. "Judging from the delegation lineup, the mission appears to place emphasis on North Korea's continuing diplomatic outreach and nuclear and security issues", Aoki said. "My administration will cooperate with the global community, including the United States, to resolve the remaining issues such as worldwide sanctions as soon as possible".
Instead, it may be more fruitful to look at what Pyongyang has actually done so far in the wake of the Singapore summit.
But progress has since stalled with Pyongyang and Washington - which stations 28,500 troops in South Korea - disagreeing over what that means.
On the issue of differences in the stances of the USA and North Korea, Moon said he believes that both sides are fully aware of each other's views but that distrust built up over the years is holding back either side from taking the first step. "I don't think it will be discussed in North-US nuclear talks".
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North Korea will 'make efforts for the second summit to achieve results that will be welcomed by the global community, ' Kim was quoted as saying by China's official Xinhua News Agency. He's had a summit with a USA leader, developed a nuclear programme and is now eyeing greater economic expansion through China. President Moon said there is no difference in understanding between Kim Jong-un and the worldwide community.