Trump canceled a North Korea trip by Secretary of State Michael Pompeo last month, a day after it was announced, citing a lack of progress.
At a landmark June summit in Singapore between Trump and Kim in, the two leaders pledged to denuclearize the Korean Peninsula but no details were agreed. The working-level talks will deal with security, communication and press-related elements of the summit, Chung said.
Narrowing the gap and rebuilding trust between Kim and Trump is key in the dialogue - if any - ahead, he said. He reportedly expressed some frustration to Chung that measures he has taken thus far, including decommissioning a nuclear test site in May, have not been taken seriously by the United States.
Since then, neither side has seemed willing to make a substantive move, leading to skepticism over Trump's claims that Kim will really dismantle his nuclear weapons program.
"Our government believes that an end-of-war declaration is very much needed while we enter a process toward stabilizing peace in the Korean Peninsula through complete denuclearization", said Chung Eui-yong, Moon's national security adviser and the head of the South Korean delegation to Pyongyang, in a news conference on Tuesday.
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Although North Korea stages military parades nearly every year, and held one just before the Olympics began in South Korea in February this year, Sunday's parade comes at a particularly sensitive time.
The officials arrived in Pyongyang at 9 a.m. and were driven to the Koryo Hotel, where they were greeted by Kim's right-hand man Kim Yong-chol and Ri Son-gwon, the chairman of the Committee for the Peaceful Reunification of the Fatherland.
"South and North agreed to hold the inter-Korean summit from September 18 to 20 in Pyongyang, and to hold working-level talks at Panmunjom next week", Chung said.
Mr. Trump said there was still reason to be optimistic.
"First, the South and the North agreed to hold a South-North Korean summit in Pyongyang between September 18-20, and to hold high-level negotiations early next week to prepare for the summit", Chung Eui-yong said of his one-day trip to the North Korean capital.
On Thursday, Pompeo that North Korea still has "enormous" work to do to meet commitments made to Trump in June to accomplish denuclearization.
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Kim believes he's earned the trust of USA though and says that moves such as ending nuclear tests and destroying an underground test site should prove that he's serious about denuclearizing. "And he said he hoped to end 70 years of hostile relationship between North Korea and the U.S. and realize denuclearization by improving the North-U.S. relationship within Trump's first term".
Asked about USA intelligence that North Korea was still advancing its weapons programmes, Pompeo noted Pyongyang had ceased its nuclear tests and test-firing missiles, which he said was a "good thing".
Seoul also wants a trilateral summit among the countries, or a four-nation meeting that also includes Beijing, to declare a formal end to the 1950-53 Korean War.
The United States, however, has said it is committed to building a peace mechanism if North Korea denuclearizes. The sign read: "Peace on the Korea Peninsula".
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