President Donald Trump shows the document that he and North Korean leader Kim Jong Un signed after their summit at the Capella Hotel on Sentosa island in Singapore June 12, 2018.
The summit being planned will be the first time in more than a decade that a South Korean leader has visited the North Korean capital.
Frustrated with the lack of progress, Trump last month cancelled Secretary of State Mike Pompeo's trip to Pyongyang after the North reportedly sent a belligerent letter to the USA leader.
Kim pledged his commitment to cooperating with President Trump during high-stakes negotiations with his South Korean counterparts Thursday, saying he hopes to "achieve denuclearization" in the near future.
Pompeo himself admitted during a visit to India on Thursday that "there is still an enormous amount of work to do".
In addition to setting a date for their meeting in Pyongyang, Moon and Kim Jong Un also agreed to open a joint liaison office at the Gaeseong industrial complex north of the border before the summit, Chung said.
Another professor, Kim Joon-hyung of Handong University, found it significant that Kim did not link his Korean War peace treaty proposal to the removal of US troops from the Korean peninsula.
While the United States maintains that efforts to improve relations between the Koreas should move in tandem with efforts to denuclearize North Korea, Moon has recently said inter-Korean engagement could take the lead.
"We are working diligently" toward the declaration, Kim said, while asking for the "understanding" of the press corps.
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After their June summit in Singapore, Trump and Kim issued a vague statement about a nuclear-free peninsula without describing when and how it would occur.
The State Department later said Pompeo was sending his newly appointed North Korea envoy, Stephen Biegun, to South Korea, China and Japan from September 10-15.
"The North and the South should further their efforts to realise the denuclearisation of the Korean peninsula", state news agency KCNA quoted him as saying.
The announcement of the September 18-20 summit - the third between the North's leader Kim and South Korean President Moon Jae-in this year - comes as USA efforts to dismantle Pyongyang's nuclear arsenal have stalled.
However, there has been no indication that Kim has offered more concrete steps towards giving up his nuclear weapons and some US officials privately doubt he is willing to abandon the arsenal.
The inter-Korean summit would come just before a gathering of world leaders at the United Nations in NY at the end of September, but Seoul said Thursday that it was unlikely Kim would attend.
"The withdrawal of the USA forces, the end of the US military presence and domination is the demand of the Korean nation and the irresistible trend of the times", it said.
"(Chairman Kim) said his faith in President Trump remains unchanged.
South Korean officials say the meeting will focus on how to achieve denuclearization of the Korean Peninsula.