Earlier, China's top diplomat Yang Jiechi told Chung that Beijing "will continue to realize the goal of denuclearization, uphold the peaceful unification of the peninsula, and solve problems through dialogue and consultation".
Cheong Wa Dae plans to iron out the main issues through talks with North Korea and the U.S.in April and May, before proceeding to four-party or six-party talks.
'I feel they're approaching this matter with caution and they need time to organise their stance'.
North Korean media mentioned a visit by a delegation from the South last week, but no coverage has been seen of Kim Jong Un's invitation to meet U.S. President Donald Trump or the South Korean president to discuss the future of Pyongyang's nuclear weapons program.
Chung said he conveyed an invitation by Moon for Xi to make a state visit to South Korea.
Xi made the comments during a meeting with South Korean National Security Office chief Chung Eui-yong, who was sent to share the outcome of his recent trips to North Korea and the United States.
The South Korean envoys are expected to explain in detail what led to the agreements to hold the summits, and what Kim has said about denuclearization.
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Yang touted the "positive changes" on the Korean peninsula.
Yang said China supports the current diplomatic efforts and added that the nuclear standoff with the North should be resolved peacefully.
China is "on the same page" with Seoul over the issues of the Korean peninsula, President Xi Jinping said on Monday, a spokesman of South Korea's presidential Blue House said.
A location has not been decided for the North Korea-U.S. summit while Kim Jong Un and Moon will meet at the truce village of Panmunjom straddling the border between the two Koreas.
South Korean Foreign Minister Kang Kyung-wha will hold talks with US Secretary of State Rex Tillerson in Washington this week to discuss their countries' planned dialogue with North Korea, the foreign ministry here said Monday.
The North's official news agency has been lauding efforts between the North and South to thaw relations, but state media has continued to warn the United States and Japan against war-mongering.