U.S. President Donald Trump and South Korean President Moon Jae-in say tensions have eased significantly since then, but Ban, who is in Tokyo for an event organized by a business group, said the crisis is not over and that North Korea should fully disclose its nuclear weapons inventory to a trusted global organization such as the worldwide Atomic Energy Agency.
After his summit with U.S. President Donald Trump on the sidelines of the G20 meeting in Argentina, South Korean President Moon Jae-in took a cautious stance over an inter-Korean project to rebuild a severed cross-border transport artery, saying it may conflict with global sanctions.
When asked about a future meeting, Trump said: "I think we're going to do one fairly (soon) - into January, February, I think".
A North Korean soldier defected to South Korea on Saturday across their heavily fortified land border, which the two sides have begun to demilitarise as relations between the Cold War-era foes warm, the South's military said.
Trump and Mr. Kim opened up dialogue on denuclearisation of the Korean peninsula after months of trading military threats and pointed barbs.
The US has urged North Korea to take concrete steps towards denuclearization, whereas Pyongyang has demanded guarantees for its survival before the signing of a peace treaty.
President Donald Trump arrives for the morning working session on the second day of the G20 economic summit on July 8, 2017, in Hamburg, Germany. It was essential that global sanctions pressure be maintained on North Korea until its complete denuclearisation was achieved, he said.
Cheong Wa Dae said Moon and Trump met for about 30 minutes in Argentina on Friday and discussed Kim's visit to Seoul as well as sanctions against North Korea.
The South Koreans and their counterparts will live in the train, inspecting two railway lines for a total of 18 days - one linking the North's southernmost Kaesong City to Sinuiju City near the Chinese border, and the other connecting Mount Kumgang near the inter-Korean border to Tumen River bordering Russian Federation in the east.
The leadership of both countries suggests that by the end of 2018 will be the connection of the railroad of the South and the North. Seoul has allocated about 57 million dollars to fix and upgrade the railway infrastructure of the DPRK.
Kim agreed to travel to Seoul after hosting Mr Moon in Pyongyang in September for their third summit this year.
National Day of Mourning for George H.W. Bush: Whats closed Wednesday
Many have also heralded Bush's 73-year marriage to his wife, Barbara Bush , who died months before her husband in April 2018. Bush, who died Friday at the age of 94, will be memorialized on Wednesday at the National Cathedral in Washington .