Al Jazeera's Rosiland Jordan, reporting from Washington DC, said "the Trump administration believes that this is an opportunity to try to move ahead and try to improve the relations with the country which it says was not too far off from being at war with the United States".
South Korean President Moon Jae-in and first lady Kim Jung-sook pose for photographs on the top of Mt. Paektu, North Korea, September 20, 2018.
As the highest peak on the Korean peninsula at about 2,750 meters (9,000 ft), Mount Paektu is the mythical origin of the Korean people, featured in South Korea's national anthem and various North Korean propaganda.
The volcano topped with a deep crater lake is at the heart of North Korea's foundation mythology and used to legitimize the Kim family's dynastic rule.
The two leaders also agreed to pursue a bid to co-host the 2032 Olympic Games, and Moon said he expects Kim Jong-un to soon become the first North Korean leader to ever visit Seoul.
USA intelligence services allege that North Korea is still enriching uranium and hawks on North Korea are disappointed about the latest meeting.
"North Korea has agreed to permanently close the Dongchang-ri engine testing and missile launch site in the presence of experts from relevant countries".
Last year Mr Trump engaged in a war of rhetoric with Mr Kim in which he threatened to destroy North Korea.
Pyongyang also said it could dismantle its best-known nuclear facility at Yongbyon, if the USA takes "corresponding measures", as Kim and the South Korean president held their third summit this year.
The question is whether it will be enough for President Donald Trump to pick up where Moon has left off. Trump told reporters Wednesday that the outcome of the summit was "very good news" and that "we're making tremendous progress" with North Korea. They then rode vehicles to the mountain on the North Korean-Chinese border.
With the main business of the day complete, North Korea was expected to hold a huge mass games spectacle in the evening, with Moon as the special guest.
Vipin Narang, an associate professor of political science at the Massachusetts Institute of Technology, tweeted that the Moon-Kim summit had made the Korean Peninsula safer.
The two sides agreed to break the impasse during Kim Jong Un's historic meeting with Trump in Singapore in June.
However, in the meantime Moon and Kim made concrete moves of their own to reduce tensions on their border. "I promised President Moon Jae-in that I will visit Seoul in the near future", he said.
They also agreed to withdraw 11 guard posts from the Demilitarized Zone by December and to establish a no-fly zone above the military demarcation line that bisects the two Koreas that would apply to planes, helicopters and drones. And in a terrifying scene, Woodward explains Graham's strategy towards North Korea with precisely what the senator is willing to give up: Namely, the people in South Korea who would be targeted by North Korea's weapons if a war did break out.