The two Koreas have informally agreed the summit will take place in Pyongyang late this month or at the beginning of September, Yonhap News Agency reported Monday, without citing a source.
Kim Eui-keum, a spokesman for Moon, said that holding the summit before September 10 would be hard due to logistics.
Unification Minister Cho Myoung-gyon is leading the South Korean delegation.
The two Koreas held a fresh round of talks at the DMZ on Monday to discuss the third summit..
"We'll at time play out a little bit, see how the talks between the North and South today go, and then see what the future holds", Harris said, noting President Moon Jae-in's remarks that the improvement in relations between North and South Korea can not advance separately from the nuclear issue.
Senior officials from the rival Koreas are meeting to set a date and venue for a third summit between South Korean President Moon Jae-in and North Korean leader Kim Jong Un.
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Pyongyang saw a second inter-Korean summit in 2007, when Roh Moo-hyun also met Kim Jong Il.
Pyongyang has previously lavishly celebrated the occasion with military parades or mass games involving thousands of people performing acrobatic choreography in unison, and is expected this time to hold its first mass games for five years, boosting tourism revenues.
North Korea is thought to have a growing arsenal of nuclear bombs and long-range missiles and to be closing in on the ability to reliably target anywhere on the US mainland. As The Korea Herald reports, on September 9, North Korea will celebrate 70 years of existence under the regime that was founded by Kim Jong Un's grandfather, Kim Il Sung.
Cho addressed the possibility of Pyongyang raising the issue of sanctions to the South, and said: 'We will explain our position to the North'.
Kim and Trump both agreed to "build a lasting and stable peace regime on the Korean Peninsula", while the North Korean leader "reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula".
Experts say there has been slow progress on those efforts since the Singapore summit.
The South Korean envoy said he urged Pyongyang to accelerate its current nuclear negotiations with the United States.