Many also believe the North has other covert nuclear facilities.
"We're talking about a package that would carry many elements, including the declaration of the facilities, Yongbyon and Tongchang-ri, which are of United States interest, and from the North side, the issues of normalising relations, ending the war and easing sanctions".
"To achieve complete denuclearisation, North Korea must permanently dismantle its nuclear facilities - including its Yongbyon facilities - and the existing nuclear warheads and missiles ..."
Last year Mr Trump engaged in a war of rhetoric with Mr Kim in which he threatened to destroy North Korea.
It features prominently in the North's propaganda, which extols the mountain as the birthplace of Kim Jong Il, the father of current leader Kim.
After two days of talks in Pyongyang, Moon and Kim on Wednesday signed a joint declaration to rid the Korean Peninsula of nuclear weapons, with the North inviting worldwide observers to witness the dismantling of the Tongchang-ri missile test site.
That was the message from South Korean President Moon Jae-in on Thursday during a news conference in Seoul to cap a historic trip to Pyongyang.
The Korean summit comes as the US effort to get North Korea to shut down its nuclear weapons program has met with mixed results. He explained that the "measures" included ending hostile policies and "guaranteeing the North's safety". Although he has made a meaningful gesture of goodwill in returning US troops' remains from the Korean War, the evidence that Kim has begun the denuclearization process in earnest is messy at best.
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The New York meeting, once firmed up, would be the first meeting between the ministers of both sides since the swearing in of Mr. PM Imran has written a letter to his Indian counterpart and sought a resumption of dialogue between the two countries.
"Chairman Kim has repeatedly expressed his strong will to denuclearise", Moon said, adding that the North Korean leader wanted to "focus on economic development" as soon as possible.
To go further, Mr. Kim has demanded "corresponding" measures from the United States, like declaring a formal end to the 1950-53 Korean War, which was halted only with a truce.
Many South Koreans also feel drawn to the volcano, which, according to Korean mythology, was the birthplace of Dangun, the founder of the first ancient Korean kingdom, and has always been considered one of the most lovely places on the peninsula.
"We're making tremendous progress with respect to North Korea".
Only hours after standing with Kim on the peak of a volcano that's at the heart of Kim dynasty propaganda, Moon told reporters in Seoul that he will be carrying a private message from Kim to Trump about the nuclear standoff when he meets the us president in NY next week on the sidelines of the U.N. General Assembly session.
"The statement clearly implies that inter-Korean summits and theatrical promises to dismantle the odd facility simply can't substitute for a negotiating process on the nuclear issue", said the Asia Society Policy Institute's Daniel Russel. Such a declaration would be the first step toward a formal peace treaty, but many in the United States are anxious that it could result in Kim pushing for the removal of USA troops stationed in South Korea to deter the North.
But there have been concerns in South Korea and the United States that ending the war would ultimately prompt China and Russian Federation, if not North Korea, to demand that the United Nations Command (UNC), which overlaps with USA forces in South Korea, be disbanded and leave.
A better-than-expected outcome of the summit between the two Koreas immediately kick-started stalled negotiations between Washington and Pyongyang, boosting President Donald Trump's high-stakes push to get the North to give up its nuclear weapons by the end of his first term in office. "We need to give him big credit for engaging in such hard challenge". "Some of the UN Security Council resolutions may be lifted, whilst Seoul may also lift unilateral sanctions", Kazianis said.