"He (Kim) also expressed his intention to put an end to the history of war and confrontation through the success of the North-US summit and to cooperate for peace and prosperity," Moon told reporters, adding both he and Kim agreed to meet or talk in person "if necessary".

Moon and Kim held a surprise summit in the Demilitarised Zone separating their two nations on Saturday in a scramble to save a slated June 12 summit between North Korea and the United States in the city-state of Singapore.

Trump rattled the region on Thursday by cancelling his meeting with Kim, citing "open hostility" from Pyongyang.

But within 24 hours he reversed course, saying it could still go ahead after productive talks were held with North Korean officials.

During his two hour meeting with Kim, Moon said he urged both Washington and Pyongyang "to remove misunderstandings through direct communication and to have sufficient dialogue in advance through working-level negotiations on the agendas to be agreed upon at the summit".

"Chairman Kim agreed on that," he added.

Moon said the Pyongyang regime reaffirmed its commitment to give up its nuclear weapons but had its own security concerns if it took that step.

"Kim stressed again that he had a firm determination towards complete denuclearisation," the South Korean president added.

"The thing he was uncertain about was not denuclearisation but concerns on whether he could trust that the US would end its hostile policy and guarantee the security of his regime when the North denuclearises itself."