"Chairman Kim Jong Un expressed hopes for a second summit with President Trump at an early date," Moon told reporters on his return to Seoul.

Kim and Trump held a historic and high-profile meeting in Singapore in June, where the North's leader committed to work towards denuclearisation of the Korean peninsula, but no details were agreed.

Washington and Pyongyang have subsequently sparred over what that means and how it will be achieved, with the Trump administration consistently referring to the denuclearisation of North Korea specifically.

The process had become deadlocked until Moon's trip to Pyongyang, where Kim agreed to permanently dismantle a missile testing site.

Experts were sceptical but the Trump administration immediately welcomed the move, with Secretary of State Mike Pompeo inviting his North Korean counterpart to meet next week on the sidelines of the United Nations General Assembly.

Kim also hoped Pompeo would soon visit the North again, Moon said, and was seeking "fast progress in denuclearisation".