A second Trump-Kim Jong Un meeting, originally expected to take place before the end of 2018, could now be less than two months away.
Ban said he hopes their second summit will occur at a time when the global community feels confident about North Korea's commitment to denuclearisation. The content of this image is as provided and can not be independently verified.
Moon said Kim visiting Seoul by the year's end may still be possible, but it would be up to Kim to decide.
Moon made the remark onboard his presidential plane that Trump asked him during their meeting Friday at the G20 in Buenos Aires to personally convey the message to Kim, reports Efe news.
South Korean soldiers open the gate as the rails which leads to North Korea is seen, inside the demilitarized zone separating the two Koreas in Paju.
President Moon Jae-in's approval rating fell last week to the lowest point since he took office in May a year ago, amid an economic slowdown and a stall in progress toward North Korea's denuclearization, a poll showed Monday.
The Koreas and the U.S. -led U.N. Command recently finished removing firearms and troops from the jointly controlled area at the border village of Panmunjom, and eventually plan to allow tourists to freely move around there.
Trump said on Air Force One while returning to Washington from Argentina that his next meeting with Kim would likely happen in January or February.
However, after hosting their third summit meeting with Moon in Pyongyang in September, Kim has agreed to visit Seoul.
Trump has frequently described a warm personal relationship with Kim, arguing that this rapport would help him succeed at a diplomatic breakthrough that has eluded USA presidents since the 1950s.
The US has given its support to the rail survey, but Mr Moon will have to have a number of hard conversations if he's to persuade President Donald Trump that easing sanctions at this stage would be worthwhile so the project can go ahead, our correspondent says.
"I think it will be absolutely imperative in this next summit that we come away with a plan for identifying all of the weapons in question, identifying all the development sites, allowing for inspections of the sites and the plan for dismantling nuclear weapons", Pence said.