The summit was held in the port city of Dalian on Monday and Tuesday, just weeks after the two took part in historic talks in Beijing.
The Kim-Xi meeting was the top news story in North Korea, with its most famous television announcer, Ri Chun Hui, again called out of her semi-retirement to report the event, underscoring its importance.
The second summit between Kim and Xi in the northern Chinese city of Dalian on Monday and Tuesday appeared to highlight efforts by the allies to restore ties that have been chilled by the North's nuclear and missile development.
"I hope to build mutual trust with the USA through dialogue", Mr Kim was quoted as saying.
The second meeting with Xi and the lack of details on the Trump-Kim summit - a time and location have still not been set, although Trump has said an announcement is coming soon - has raised speculation among analysts that the summit preparations may have hit a snag.
In a text message to reporters, Moon's spokesman, Kim Eui-kyeom, said China had informed South Korea of the Dalian summit. "In particular, I think dialogue between Japan and North Korea should be resumed", Moon said in the interview with the Yomiuri newspaper.
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Israel claims all of Jerusalem as its "eternal and undivided" capital which it captured from Jordan in the Six Day War in 1967. Trump has left the question of his participation in the embassy opening in doubt for months, saying that he might come.
China has been largely sidelined by the developments between the two Koreas and the U.S., and will be keen to ensure the North does not get too close to Washington, which it sees as a competitor in the region.
"China supports North Korea's upholding of denuclearisation on the peninsula, and supports North Korea and the United States resolving the peninsula issue through dialogue and consultation", Xi said.
U.S. President Donald Trump said he will discuss trade with Chinese President Xi Jinping on Tuesday, as both sides continue talks after failing to reach a consensus at talks in Beijing last week, Reuters reports.
In a cordial and friendly atmosphere, the two leaders had an all-round and in-depth exchange of views on China-North Korea relations and major issues of common concern, it said.
The visit followed a dramatic visit by Kim to Beijing in March, and comes ahead of a planned summit meeting between Kim and U.S. President Donald Trump.
The Chinese foreign ministry would not confirm or deny that a North Korean official had visited the country. "Maybe it won't. But it can be a great thing for North Korea, South Korea and the entire world".
Though rumors are likely widespread, North Korea's media still have not explicitly confirmed the expected summit with Trump.
South Korea's Yonhap News Agency said North Korean leader Kim Jong Un may have been aboard the plane, although it cited no direct evidence. Others claimed to have spotted Red Flag limousines used by the statesmen, AP said.