Hong Kong-based South China Morning Post cited two unofficial sources to say that Jinping went to Dalian to meet the guest official and preside over the launch of sea trials for China's inaugural aircraft carrier, built entirely indigenously.
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.
Donald Trump is also due to speak to President Xi today via telephone in a conversation which will include North Korea.
Within a period of more than one month, he and Kim met twice and they have been keeping in close contact, Xi said.
Mr Kim is quoted as saying: "These are the positive outcomes of the historic meeting between me and Comrade General Secretary (Xi)".
Meanwhile, US President Donald Trump tweeted that he will be speaking to Chinese President Xi Jinping about trade and North Korea.
In a text message to reporters, Moon's spokesman, Kim Eui-kyeom, said China had informed South Korea of the Dalian summit.
Japan's Kyodo News service said the plane departed on Tuesday. It said the USA was inconsistent in its approach two cases of nuclear proliferation in the world - one in Iran and other in North Korea and China feels its role could play big if the US's unpredictability fails to serve the real cause.
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But our future is not in our hands. "We have to try and get three points to apply pressure". Our opponents are dropping points, but our vision is not in our hands.
It was Kim's second visit to China since March, highlighting efforts by the two countries to mend ties that had soured after Beijing supported United Nations sanctions against North Korea for its nuclear-weapons tests.
CCTV quoted Mr Xi as saying China "supports North Korea to stick to denuclearisation of the Korean Peninsula and supports North Korea and the U.S. in solving the peninsula issue through dialogue and consultation".
The North Korean official flew in a private plane and arrived at Dalian airport on Monday amid heavy security, Yonhap said.
Foley pointed out that North Korea has made numerous promises of going nuclear-free in past decades as well, with hopes of peace never actually materializing.
The Chinese foreign ministry would not confirm or deny that a North Korean official had visited the country.
The official Xinhua news agency said the two leaders met on both May 7 and May 8.
It is not clear when the meeting was planned or put together or why Dalian was chosen. Others said they spotted a set of Red Flag limousines used by state leaders.