The South Korean President on Sunday proposed holding a trilateral summit with Washington and Pyongyang to try to formally end the Korean War, once the meeting between the US and the North is "successful."

"Should the North Korea-US summit succeed, I would like to see efforts to formally end the (Korean) war through a three-way summit of the South, the North and the US," Moon Jae-in said at a press conference, referring to the fact that South and North Korea technically are still at war as the 1950-53 Korean War ended only with an armistice.

Moon also explained that Kim is unsure about the security guarantees offered by the US in exchange for denuclearization.

"What remains uncertain to Chairman Kim Jong-un is whether he can trust the US promise to end their hostile relationship and guarantee North Korea's security once the North denuclearizes," Moon said.

Moon appeared before the media in Seoul on Sunday to explain the content of his surprise meeting on Saturday with North Korean leader Kim Jong-un, in which both pledged to work together to make the summit between Washington and Pyongyang scheduled for 12 June in Singapore "a success".