South Korean President Moon Jae-in on Tuesday hailed the third meeting between US President Donald Trump and North Korean leader Kim Jong-un in the Demilitarized Zone as the result of an "astounding imagination" and thinking outside the box.

All three held an impromptu encounter at the truce village of Panmunjom on Sunday when Trump became the first sitting US president to set foot in North Korea and agreed with Kim to resume working-level talks, which had been deadlocked since their second summit in Hanoi in February.

The gathering was proposed by Trump via Twitter a day earlier, offering to meet Kim at the border to "say hello," with the North delivering an unusually fast response.

Moon praised both men's actions. "That extraordinary proposal and bold response is the result of an astounding imagination that goes beyond common sense," Moon said. 

"This is unthinkable in the existing diplomatic grammar."

It was a "de-facto declaration of an end to hostile relations and the beginning of a full-fledged era of peace," said Moon, who has long promoted engagement with Pyongyang.

Moon was instrumental in brokering the landmark summit between Trump and Kim - the first meeting between a sitting US president and a North Korean leader - in Singapore last year, which produced a vaguely-worded pledge about denuclearization.