The South Korean delegation for Monday's talks is led by Cho Myoung-gyon, who oversees Seoul's Unification Ministry that handles inter-Korean issues, and includes Nam Gwan-pyo, a Moon aide responsible for North Korean nuclear matters.
Moon will be the third South Korean president to travel to the North Korean capital.
In opening remarks, the head of the North Korean delegation set a positive tone for the day's meeting, comparing the current state of inter-Korean relations to very close friends where nothing can stand between the two.
Global sanctions against the North for its nuclear and missile programmes have kept economic cooperation between the two Koreas from taking off, while little progress has been made on the key issue of Pyongyang's denuclearisation.
After Monday's talks, Ri Son Gwon, the chairman of a North Korean committee aiming for the "peaceful reunification" of the peninsula, told his South Korean counterpart, Unification Minister Cho Myoung-gyon, it was important to clear "obstacles" preventing inter-Korean relations from moving forward.
The two sides held historic meetings in April and May, at the border truce village of Panmunjom, within the demilitarised zone (DMZ) that separates the two countries.
North and South Korea agreed on Monday (Aug 13) to hold a summit in Pyongyang in September after high-level talks in the Demilitarized Zone that divides the peninsula. Former South Korean President Roh Moo-hyun also met Kim Jong Il in Pyongyang in 2007.
"We explained that we need to help North Korea-US talks progress quickly and that there needs to be an establishment of dynamic where the inter-Korean relationship and the North Korea-US relationship improves in cycles", he said.
The summit would probably be held after the 70th anniversary of the North's foundation on September 9, the South's presidential office suggested.
"We also reviewed the implementation situations of the Panmunjom Declaration and held consultations in a honest manner on matters related to its more active enforcement", they added, referring to the agreement reached at the historic April summit. Meanwhile the U.S. has urged the global community to maintain tough sanctions on the isolated regime.
Analysts say Moon could try to act as a mediator between the U.S. and North Korea, having salvaged the Singapore meeting when Trump abruptly cancelled it.
The North has called for Seoul to fulfill its promise of declaring an end to the war as soon as possible, while the USA has said that the North should take meaningful denuclearization steps first.
Despite the rapprochement, global sanctions against the North for its nuclear and missile programmes have kept economic cooperation between the two Koreas from taking off, while little progress has been made on the key issue of Pyongyang's denuclearisation.
But Harry Harris, the U.S. ambassador to South Korea, said on Monday it was "too early" for such a declaration, Yonhap reported. Sanctions will remain in place until North Korea takes concrete and verifiable steps toward denuclearisation.