North and South Korean officials held high-level negotiations at the border truce village of Panmunjom on Monday to discuss the summit.
In a three-sentence joint statement, the rival neighbours didn’t mention an exact date for the meeting and provided no details on how to implement past agreements.
The push for what will be the leaders’ third summit since April comes amid renewed concerns about a nuclear standoff between Washington and Pyongyang.
“The September summit can be viewed as North Korea’s strategy to find a breakthrough in its stalled talks with the US,” said analyst Go Myong-hyun from the Asan Institute of Policy Studies.
“For South Korea, President Moon wants to improve inter-Korean ties, but that’s hard without progress in US-North Korea talks,” he told AFP news agency.
Moon’s trip to Pyongyang will be the first in more than a decade.
The first South Korean president to go to the North’s capital was Kim Dae-jung, who met the current leader’s father and predecessor Kim Jong-il in 2000 and later won the Nobel Peace Prize in part for his efforts at inter-Korean reconciliation.
Pyongyang saw a second inter-Korean summit in 2007 when Roh Moo-hyun also met Kim Jong-il.
But relations subsequently soured as the North accelerated its pursuit of nuclear weapons and the South elected conservative governments.
Kim and Moon met for the first time in April and agreed on steps towards nuclear disarmament. They met again in May in advance of Kim’s summit with US President Donald Trump in Singapore.
At their meeting in April, Kim and Moon signed a Panmunjom Declaration that calls for a formal end to the 1950-53 Korean War and included a pledge to denuclearise the peninsula.
Pyongyang has 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.