South Korea's President says North Korean leader Kim Jong Un remains committed to holding a summit with US President Donald Trump and to the "complete denuclearisation of the Korean Peninsula."

Moon Jae In met Kim at the border for the second time in a month to discuss how to keep Kim's summit with Trump on a track.

The Kim-Moon meeting followed a whirlwind 24 hours that saw Trump cancel the highly anticipated June 12 meeting on Friday before saying it's potentially back on.

Moon told reporters today that Kim reaffirmed his denuclearisation commitment and told Moon he's willing to cooperate to end confrontation for the sake of the successful North Korea-US summit.

Moon says his meeting with Kim was arranged at Kim's request.

Trump now says negotiations over a potential summit with Kim are "going along very well."

Trump told reporters that: "We're doing very well in terms of the summit with North Korea," adding that "there are meetings going on as we speak."

Trump said they are still considering June 12 in Singapore for the summit.