Calling the Singapore summit the "starting point", Harris reiterated Trump's belief in the North Korean leader's commitment to denuclearization and the communist state's potential to lift itself out of poverty and have a brighter future should Kim fulfill his commitment.
No date was given for the forthcoming summit, which was announced after talks at the border between the two states.
Cho, the chief of the South Korean delegation, said the two sides also "talked a lot" about worldwide sanctions meant to punish the North for its development of nuclear weapons, but he didn't elaborate.
The two Koreas held a fresh round of talks at the DMZ today to discuss the third summit, which will be held in September, It was led by the South's Unification Minister Cho Myoung-gyon and Ri Son Gwon, chairman of the North's reunification committee.
The summit meeting, if held, will mark the third of its kind between South Korean President Moon Jae-in and North Korean leader Kim Jong-un following their face-to-face meetings in April and May.
North and South Korea agreed to hold a summit in Pyongyang in September, the latest step forward in cross-border ties this year after more high-level talks on Monday (Aug 13), the South's Unification Ministry said.
The agreement was made during high-level talks on the northern side of Panmunjom that separates the two Koreas.
If the summit occurs, it would be the third since April, when the once-rival countries began thawing tensions after almost reaching the brink of nuclear war.
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North Korea, which proposed Monday's talks last week, also sent officials overseeing past inter-Korean economic collaborations. "As President Moon stated, "the improvement of relations between North and South Korea can not advance separately from resolving North Korea's nuclear program'".
The overture culminated in a historic summit between Kim and U.S. President Donald Trump in June, where they signed a vague agreement for the North to rid itself of its nuclear arsenal. The Seoul government appears reluctant to push for full-blown cooperation with the North, constrained by multilayered sanctions imposed on Pyongyang.
Senior diplomatic sources told CNN last week that Pyongyang has continually rejected Washington's proposals on denuclearization, calling them "gangster-like".
Cho, however, said there were no new details on the progress.
Kim and South Korea President Moon Jae-in have already met twice his year, with the second meeting setting up the Trump-Kim summit.
Experts say there has been slow progress on those efforts since the Singapore summit.
The North has urged the United States to end the sanctions, saying it had made goodwill gestures, including a moratorium on nuclear and missile tests, the dismantling of a nuclear site, and the return of the remains of some US soldiers killed in the Korean War.