In proposing the minister-level talks, the North made it clear that it wanted to discuss matters related to another meeting between the two leaders and follow-up measures to the Panmunjom Declaration they signed after their April 27 summit.
North and South Korea say their respective leaders will meet in North's capital of Pyongyang sometime next month.
The talks Monday are happening at a North Korea-controlled building in the border village of Panmunjom.
The leaders of North and South Korea will hold their third summit in September, officials from the two countries announced Monday.
Pyongyang has urged Washington to ease the economic punishments, but the United States says that can not happen until the North completely denuclearises.
Mr Moon, the only South Korean leader to have met a North Korean leader twice, will become the first leader to visit Pyongyang this year.
"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.
Cho, the South Korean reunification minister, said North and South Korea discussed denuclearization in general terms during their talks Monday.
But while the declaration that followed Trump's meeting with Kim was widely criticized for being too vague, the Panmunjom Declaration reached between Moon and Kim was much more detailed, Delury said. They met again in May in advance of Kim's summit with US President Donald Trump in Singapore.
Cross-border exchanges between the two Koreas have significantly increased since then, with the neighbors planning to hold reunions for war-separated families next week for the first time in three years.
Conversations over a permanent peace treaty to end the Korean War will be ongoing, with speculation suggesting that the North is pushing for concrete progress on this front before committing to additional disarmament.
The Kim regime takes issue with the Trump administration's support of worldwide sanctions impacting the country; reaction from Bill Richardson, former US ambassador to the United Nations.
The ministry official said that the government plans to report its probe results on the alleged illegal shipments to the UN Security Council's sanctions committee as early as this week, adding the USA has already been briefed on the matter.