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 United States efforts to dismantle Pyongyang's nuclear arsenal have stalled.
Kim told South Korean officials his faith in Trump was "unchanged" and he wanted denuclearization and an end to hostile relations with the United States within Trump's first term in office, ending in early 2021, Chung said.
Trump's comments came after Kim reportedly said his faith in the U.S. president was unchanged and that Pyongyang aimed to achieve denuclearisation within Trump's first term in office, which is due to end in January 2020.
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.
At a news conference aired on South Korean TV and reported by the South Korean news agency Yonhap, the envoy, Chung Eui-yong, said the meeting - the third between the two leaders - would be September 18 to 20 in Pyongyang.
He says Trump asked South Korean President Moon Jae-in to work as "chief negotiator" to mediate between Washington and Pyongyang during their earlier phone talks.
Now, the South Korean envoy has a message for Trump from Kim, who apparently described the steps his country has made toward denuclearization as "very significant and meaningful", Yonhap reported.
"Chairman Kim. expressed frustration over the doubt shown by some parts of the global society about his will", Chung said.
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The South Korean envoy's visit to Pyongyang came amid a deadlock on the North's atomic weapons, with U.S. efforts to dismantle the arsenal stalled for weeks.
On the one-day trip, the five-member delegation, which also included National Intelligence Service Director Suh Hoon, met with Kim and top North Korean officials including Kim Yong-chol, vice chairman of North Korea's ruling Workers' Party. The milestone meeting resulted in an accord, sealed by Trump and Kim, in Singapore in June, but the talks between Pyongyang and Washington stalled as both sides disagreed on how to carry out the vaguely-worded agreement.
In New Delhi Thursday, Secretary of State Pompeo, the former U.S. intelligence chief who heads the USA negotiating effort, struck a sober note, saying there is still much work to do. And it won't until Pyongyang gives up its nuclear weapons, the USA says.
The U.S. Embassy in Seoul on Thursday said it had no information to share on the matter.
The North's Rodong Sinmun newspaper on Thursday said Washington must discard its "stubborn" stance that the North must denuclearize first before the United States agrees to a peace treaty. He also said, on the basis of such trust, he hopes to end 70 years of hostile relations with the United States, improve the bilateral relationship and fulfill denuclearization, ' he said.
Under discussion is whether denuclearisation or declaring an end to the 1950-53 Korean War should come first. -South Korean alliance or lead to the withdrawal of the 28,500 USA troops stationed in South Korea to prevent North Korean attack, according to Mr. Chung. The U.S. president gave Moon's envoys a message to deliver to Kim Jong Un, who gave the officials a statement to send to the White House.
"It is the case that there is still an enormous amount of work to do", Pompeo told a news conference in New Delhi.
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