But discussions over how to implement the vague commitments have since faltered.
The question hovering over their talks this week has been whether Kim would agree to take steps to convince Washington that he is willing to denuclearize.
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South Korean President Moon Jae-in, right, and North Korean leader Kim Jong Un walk together at the Paekhwawon State Guesthouse in Pyongyang, North Korea, Wednesday, Sept. 19, 2018. "In the meantime there will be no rocket or nuclear testing", Trump wrote on Twitter.
It would be the first-ever visit to the South Korean capital by a North Korean head of state.
Kim said both sides agreed to closely cooperate to open a new era of peace and prosperity through their "historical summit" by ending hatred and conflict between the two Koreas caused by their tragic national division.
Trump has been positive about his relationship with Kim personally, but canceled US Secretary of State Mike Pompeo's last visit to Pyongyang, citing lack of progress on denuclearization.
He also visited the White House earlier this year as the US and North Korea prepared for June's historic summit.
Pyongyang is said to be demanding early rewards for denuclearization steps it has taken so far, while Washington continues to stress the importance of maximum pressure and sanctions against the North until the communist state fully denuclearizes. On Wednesday, the Korean leaders signed a joint statement supporting a nuclear weapon-free peninsula to "eliminate all the danger of war", the Associated Press reports.
Also at the UN General Assembly, Moon is expected to meet and brief Trump - who, according to Moon's aides, has called the South Korean president a "chief negotiator' between himself and Kim". Such a trip would be the first by any North Korean leader, another dramatic moment in the flurry of diplomacy around the North's nuclear weapons program in recent months.
Andrew Lankov, a professor at Kookmin University in Seoul, said it would take time to understand the significance of what Kim was offering, especially in relation to its Yongbyon facility, home to the country's only nuclear reactor and key to its production of weapons-grade plutonium - although other sites are believed to exist producing highly enriched uranium.
But Mr Trump's late-night tweets did not address the U.S. matching North Korea's moves.
Both countries made a decision to open a permanent meeting place for families long separated by the border in the near future, Moon said.
The institution was sanctioned by the U.N. Security Council previous year as part of global efforts to rein in Pyongyang's nuclear and missile programs by drying up its revenue sources.
Seo Yu-suk, a research manager at the Institute of North Korean Studies in Seoul, said the facilities at Dongchang-ri and Yongbyon are "almost obsolete" and the North has mobile missile launchers that are easier to use and harder to detect, while there are likely covert sites elsewhere.
Talks in Pyongyang built on a growing rapprochement, with the two leaders agreeing Wednesday to hold family reunions on a regular basis, work towards joining up road and rail links, and mount a combined bid for the 2032 Olympics.
They also adopted a separate military accord aimed at preventing armed clashes between the old foes, which are technically still at war because the Korean War ended with a truce, not a peace treaty.
They also agreed to halt military drills near the military demarcation line, withdraw some border guard posts, disarm the Joint Security Area in the Demilitarized Zone and jointly excavate war remains in the buffer zone.