Kim told South Korean officials his faith in Trump was "unchanged" and that he wanted denuclearisation of the Korean peninsula and an end to hostile relations with the United States before Trump's first term in office ends in early 2021, Chung said.
Moon, who brokered the historic summit between Kim and Trump in Singapore, said he had "high hopes" for his next meeting with the North's leader to achieve a similar feat. They're not discussing the contents of the messages.
Pompeo, visiting New Delhi, said there was a long road ahead and "an enormous amount of work to do" on the denuclearisation process.
Chung said the upcoming summit will review the implementation of the inter-Korean summit agreement reached at the leaders' first meeting in Panmunjom.
Another professor, Kim Joon-hyung of Handong University, found it significant that Kim did not link his Korean War peace treaty proposal to the removal of USA troops from the Korean peninsula.
"Chairman Kim emphasized that he has never made a negative comment about Trump", Chung Eui-yong, South Korea's top national security adviser, said at a media briefing on Thursday.
The newly appointed United States envoy for the North, Stephen Biegun, last month said Kim had promised "final, fully verified denuclearization" at the summit.
At a press conference, the envoys said Mr Kim told them it was his firm will to work with South Korea to achieve a lasting peace settlement.
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Two senior members of South Korea's delegation to Pyongyang are to fly to China and Japan to brief them on their meeting with Kim.
The newly appointed US special envoy for North Korea will make his first diplomatic trip overseas next week in the Trump administration's latest effort to press for progress in uncertain denuclearization talks.
According to South Korea's National Election Survey Deliberation Commission, Moon's approval rating now stands at 49 percent, local newspaper Hankyoreh reported.
The Associated Press reports that Chung said Kim expressed frustration over the worldwide community's reaction to measures taken by the North.
A peace declaration could put the U.S.in a tricky position.
North Korea and the United States have since cooled their feud as Kim and Trump both extended olive branches this year - culminating in a summit in Singapore. South Korean President Moon Jae-in also agreed to meet Kim in the North Korean capital on September 18-20, the first such trip in 11 years.
That message will very likely contain an appeal for Washington to formally declare an end to the war - something Pyongyang says is vital to building trust and ending decades of hostility.
"The withdrawal of the USA forces, the end of the US military presence and domination is the demand of the Korean nation and the irresistible trend of the times", it said.
"While these talks are military-to-military and scheduled to be confined to the repatriation issue, having some progress on any front would be welcome", the USA official said, speaking on the condition of anonymity.