Mr Kim has been visiting Beijing this week to project an image of a strong Pyongyang-Beijing alliance in advance of a second potential summit.
Mr Xi said China supported North Korea and the U.S. "holding summits and achieving results, and supports relevant parties resolving their respective legitimate concerns through dialogue".
Details of what Kim and Xi discussed have yet to be revealed, but their summit is seen as an opportunity to strategize ahead of a second North Korea-U.S. summit meant to move along denuclearization negotiations.
Like his father - Kim Jong-il, who ruled North Korea from 1994 to 2011, Kim's strength has always been his "vagueness" about what he'll do next, and an ability to "keep everybody guessing until they do it", said James Kim.
Little progress has been made between the USA and North Korea since the celebrated Singapore summit last June, the very first meeting between a North Korean leader and a sitting U.S. president.
Still, China has denied any interest in using North Korea as a bargaining chip and doing so risked undermining a source of stability in its strained relations with the U.S.
Tuesday's meeting focused on Kim's expected meeting with Trump, according to Yonhap.
He also said China would be ready to play a "positive and constructive role" towards maintaining peace and achieving denuclearisation on the Korean peninsula, reported Xinhua.
China, which wouldn't want to be left out in the cold in any settlement, has worked to improve relations with its neighbour, which deteriorated after Beijing backed United Nations sanctions against North Korea. The visit wrapped up Kim's two-day stay in the city, after he met with Chinese President Xi Jinping, Tuesday.
In an interview with CNBC on Monday, US Secretary of State Mike Pompeo praised China's support for resolving the North Korean crisis and said he did not think the US trade dispute with China would affect this.More news: Kliff Kingsbury To Interview With Cardinals, Jets
The motorcade of North Korean leader Kim Jong Un has headed out on the second full day of his visit to China.
Seoul would cooperate with the United States and global community to seek to "resolve" the issue of sanctions "as soon as possible", Moon said.
All aboard: Kim's personal train which brought him to Beijing has pink leather chairs inside.
But he also urged the US President to consider issuing a formal declaration which would officially end the 1950-53 Korean War, which he suggested would encourage Kim to scrap its nuclear weapons.
In a New Year's address, Kim pledged his commitment to complete denuclearization in a message to Washington and expressed his desire to meet again with Trump - a sentiment immediately reciprocated by the US president over Twitter.
North Korean state media reported Thursday that Xi accepted Kim's invite to visit, but this was conspicuously absent from Chinese media reports.
According to North Korean's official KCNA agency China supported the North's position.
Xi greeted Kim at Beijing's ornate Great Hall of the People on Tuesday - believed to be the North Korean leader's birthday.
"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".