"We agreed to hold an inter-Korean summit within September in Pyongyang", the two sides said in a joint press statement issued after their delegations held talks in Panmunjom on Monday, according to Yonhap.
A unification flag hangs on a military fence near the demilitarized zone (DMZ) separating the two Koreas in Paju, South Korea January 15, 2018.
North Korea's chief delegate, Ri Son Gwon, had hinted a date for the summit was set, but refused to unveil the date because he wanted to "keep reporters wondering".
At the leaders' first meeting in April, at the border village of Panmunjom, Mr Moon agreed to visit Pyongyang this autumn.
Cho addressed the possibility of Pyongyang raising the issue of sanctions to the South, and said: "We will explain our position to the North".More news: Unai Emery Hints At Starting Youngster Against Manchester City
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 USA mainland.
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.
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".
He also promised to make the breeding of North Korean cattle a "state issue", and apparently offered his own expert advice on how to manage the cows.
Monday's high-level talks were proposed by the North last week as it lashed out at Washington for pushing ahead with sanctions. The North said it was making efforts to disarm, but Cho said there were no new details on those efforts.
North Korea recently returned the possible remains of US troops from the Korean War.More news: The Google Play Store Now Directly Tells You Fortnite Isn't Available
Pyongyang urged Washington to reciprocate its goodwill gestures, which include suspending missile and nuclear tests and returning the remains of Americans who fought in the Korean War.
This photo taken by the joint press corps shows South Korea's Unification Minister Cho Myoung-gyon (L) shaking hands with his North Korean counterpart Ri Son-gwon before launching high-level talks on August 13, 2018, on the northern side of Panmunjom to discuss inter-Korean relations and preparations for a summit meeting between their leaders.
"It's business as usual", the official said, showing Kim may be going against the promises he made in recent months.
"We will listen to the North's stance on the inter-Korean summit for this fall, which is agreed upon in the Panmunjom declaration, and share our views", Cho told reporters before heading to the border, referring to the agreement at the April summit.
Kim Eui-kyeom, a spokesman of South Korea's presidential office, said it would be hard for the summit to happen before the September 9 anniversary of North Korea's founding, a major holiday there.More news: Thomas Markle fears he won't see royal daughter Meghan again: Sun