The past two summits, one in 2000 and the other in 2007, were held between Kim's late father, Kim Jong Il, and two liberal South Korean presidents.
On the North Korea side, Kim was joined by his wife, Ri Sol Ju, and his sister, Kim Yo Jong, who was part of the Winter Olympics delegation and became the first member of the Pyongyang's ruling family to visit South Korea since the war in the 1950s.
However Nauert's statement illustrated the US's desire to keep applying pressure on Pyongyang over its pursuit of weapons of mass destruction (WMD).
That North Korea has resorted to inefficient and costly ship-to-ship transfers to evade the sanctions is yet more evidence that they are biting.
Tensions rose to the highest level in years over North Korea's nuclear and missile programmes, which it pursues in defiance of UN Security Council resolutions, with shrill, bellicose rhetoric coming from both Kim Jong Un and Trump.
Steam plumes were observed from the reactor in images from Feb. 17 and 28 and that such vapour plumes had "generally been a useful indicator of reactor operations", 38 North said in a report on Monday.
He spent much of his time in the Chinese gambling hub of Macau and it is not clear why he may have left the relative safety of China's protection to travel to Malaysia if he thought his life was at risk. What we need from the North is deeds, not words.
Denuclearization is Trump Administration short hand for America's strategic goal on the Korean peninsula - no nuclear weapons in either the North or the South. He said he could not adequately assess the South's account of the Pyongyang talks until the South Koreans have provided a full briefing. Head of the presidential National Security Office Chung Eui-yong and National Intelligence Service chief Suh Hoon will likely stay there for a day and explore the possibility of U.S. -North Korea talks.
US President Donald Trump has said the developments, including North Korea's suggestion that it might discuss getting rid of its nuclear weapons, "are positive" but might be a "false hope".
"By referring to the wishes of the forefathers, all internal conflict has been eliminated", Koo said, adding: "That's the best card Kim Jong Un can use".
Our maximum pressure campaign on North Korea must continue.
Chung said the two Koreas would hold a summit at a South Korea-controlled facility.
Possibilities include that the United States modify its annual drills with South Korea, stop dispatching nuclear bombers, submarines and carriers to the region and declare that it won't attack the North.
North Korea's rapid move from the Olympics' political theatrics to publicly acknowledging substantial issues and expressing a willingness to address them isn't decisive, but it is encouraging. A U.S. official said there were no plans to scrap the war games envisioned for next month. And achieving its nuclear aims rests on the North resuming tests of missiles and bombs that set the region on edge.
China, which is North Korea's only major ally, cheered the exchanges between the Koreas and called for a return to six-nation talks on denuclearization that it previously hosted.
North Korea has agreed to halt any nuclear and missile testing while talks are ongoing.
The deal fell apart in 2002 when a senior U.S. official said North Korean officials admitted to having a secret nuclear program during his visit to Pyongyang.
Chung said the two Koreas agreed to hold their summit at a Seoul-controlled facility.
The brazen daylight assassination unleashed diplomatic shockwaves and widespread condemnation of North Korea.