"We will make this trip a chance to create a firm basis for cooperation peace between the North and South", South Korean Unification Minister Cho Myoung-gyon told reporters before departure, according to Yonhap News.
South Korea's presidential Blue House has been forcefully arguing for an end-of-war declaration, and predicts that such a declaration could come after Trump and Kim meet.
U.S. Secretary of State Mike Pompeo is now scheduled to meet North Korean leader Kim Jong Un on Sunday where the men are expected to negotiate another summit between Trump and Kim.
It is part of a wider pattern of malicious state-backed cyber activity that has led the Trump administration to identify North Korea - along with Russia, Iran and China - as one of the main online threats facing the United States.
On the sidelines, Minister Cho, who is in charge of inter-Korean affairs, is expected to meet with his North Korean counterpart, Ri Son-gwon, to discuss follow-up measures to the agreement their leaders reached in their September summit in Pyongyang.
The foreign minister told the UNGA that US attempts to coerce North Korea into denuclearization will not work and that corresponding steps must be taken by both sides in order to advance progress between the two countries.
"I'm very happy to be going back to get another chance to continue to advance the commitment that Chairman Kim and President Trump made back in Singapore in the second week of June", Pompeo told a news briefing at the State Department.
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Even some skeptics, though, acknowledge that the current dialogue has brought rewards in terms of an end to nuclear and missile testing and reduced tensions. That left Seoul lobbying hard for a second summit between Trump and Kim to keep alive a positive atmosphere for nuclear diplomacy.
During their three-day stay, they will also tour major facilities and attend a mass gymnastics performance.
Kim has committed to give up his country's nuclear weapons although his actions have fallen short of Washington's demands for a complete inventory of North Korea's weapons programs and irreversible steps to give up a nuclear arsenal that potentially threatens the United States.
KCNA said the Yongbyon nuclear facility, which the North expressed a willingness to take offline if the United States takes corresponding action, "is a core one for its nuclear programme".
Pompeo stressed that, in the meantime, worldwide sanctions would have to remain in place on North Korea.
"They really have the potential" to be an economic power, Trump said.
South Korea delegation members, foreground, are welcomed on their arrival at the Pyongyang Airport in Pyongyang, North Korea Thursday, Oct. 4, 2018.