Pyongyang and Washington have been locked in a stalemate over how to carry out the agreements they reached in their first-ever summit in June, at which Kim promised to work toward complete denuclearization in exchange for security guarantees from the US. Negotiations have made little headway since.
But many analysts say that restarting the schemes would at present violate sanctions imposed on the North over its nuclear and ballistic missile programs.
"The political settlement of the peninsula issue faces a rare historic opportunity", Mr Xi said.
"Corresponding measures must be devised in order to facilitate North Korea's continued denuclearization efforts", he added, such as the United States agreeing a "peace regime" and formally declaring an end to the 1950-53 Korean War. Keeping in mind that China is North Korea's only solid, powerful ally and Kim relies on them for much of his sputtering economy, Xi Jinping has significant leverage over North Korea.
Kim reiterated a pledge from his New Year's speech that the North would try to make a second summit achieve a result that the worldwide community would welcome, Xinhua said.
The North Korean leader's trip to China this week was a sign a second Trump-Kim summit was "imminent", he added.
While Mr. Trump says he considers Xi key to enticing Kim into taking concrete steps toward denuclearization, the president's own relationship with his Chinese counterpart has frayed over the U.S. "We've had another visit (by Kim), so why is it that Xi Jinping has not gone to Pyongyang and what would it take in order for that visit to actually take place?" said Glaser of the CSIS. He also visited a pharmaceutical plant specialising in Chinese medicine.
North Korea wants relief from the multiple sets of sanctions imposed on it over its nuclear weapon and ballistic missile programs, while the U.S. wants them to remain in place until it gives up its arms - something Pyongyang has made no public promise to do.
"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". -North Korea summit and expressed hopes of further improvements in diplomatic ties and steps toward denuclearization of North Korea.
While Beijing has been angered by Kim's nuclear tests, it would not be happy to see its decades-old ally move closer to the United States at China's expense.
Xi told Kim North Korea's reasonable demands must be resolved, KCNA said.
"The path toward peace on the Korean Peninsula still continues to expand even at this moment, and it will speed up even more this year".
Xi was quoted as saying that China supports the U.S.
The North's Korean Central News Agency reported that Kim told Xi that the North remains unchanged in its push to seek a negotiated resolution of the nuclear standoff.
Following their historic meeting in Singapore last June, negotiations have somewhat stalled, as the White House demands that North Korea dismantle its nuclear program first, before the USA would lift any of its punitive measures on the country. The Xinhua report did not elaborate. His delegation was seen off by high-ranking Chinese officials and honour guard at a Beijing train station and could return to North Korea as soon as Thursday morning, Yonhap said.
However, he said reducing US military commitments, such as a withdrawal of troops or strategic assets from the region, would be unlikely options for Washington.
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.