The two leaders are set to meet by the end of May
US President Donald Trump has said a deal with North Korea could be a "very good one for the world", a day after he agreed to meet Kim Jong Un for denuclearisation talks.
He tweeted on Saturday: "The deal with North Korea is very much in the making and will be, if completed, a very good one for the World. Time and place to be determined."
The deal with North Korea is very much in the making and will be, if completed, a very good one for the World. Time and place to be determined.— Donald J. Trump (@realDonaldTrump) March 10, 2018
It comes after South Korea's national security adviser, Chung Eui Yong, informed the White House of Mr Kim's desire to meet Mr Trump and his "commitment to denuclearisation".
Mr Trump's latest comments come after the White House tried to dismiss criticism that the US was getting nothing in return for agreeing to a summit with the North Korean leader.
White House Press Secretary Sarah Huckabee Sanders reminded reporters that North Korea had committed to denuclearisation, promised to stop missile testing, and allow US-South Korea military exercises to continue.
She said: "Let's not forget that the North Koreans did promise something... We are not going to have this meeting take place until we see concrete actions that match the words and the rhetoric of North Korea."
On Friday, the White House also confirmed Mr Trump had discussed the North Korea issue with Chinese President Xi Jinping and "welcomed the prospect" of a dialogue, despite no serving US President having ever met a North Korean leader.
They also committed to maintaining pressure and sanctions until North Korea takes "tangible steps" towards "complete, verifiable and irreversible denuclearisation".
White House legislative affairs director Marc Short said President Trump's decision to meet Mr Kim was made with a "handful" of lawmakers.
He said while the White House hoped the encounter would "bear fruit", officials remained "cautious".
The historic meeting - expected to take place by May - comes after the two leaders traded insults for months and economic sanctions on North Korea being tightened.
Mr Trump had previously threatened "fire and fury" in response to threats from North Korea and referred to Kim Jong Un as "Little Rocket Man", while Mr Kim called the US president a "dotard".
But on Friday, the US leader tweeted: "Kim Jong Un talked about denuclearisation with the South Korean representatives, not just a freeze.
"Also, no missile testing by North Korea during this period of time. Great progress being made but sanctions will remain until an agreement is reached. Meeting being planned!"
Kim Jong Un talked about denuclearization with the South Korean Representatives, not just a freeze. Also, no missile testing by North Korea during this period of time. Great progress being made but sanctions will remain until an agreement is reached. Meeting being planned!— Donald J. Trump (@realDonaldTrump) March 9, 2018
US Vice President Mike Pence said the move was "evidence that President Trump's strategy to isolate the Kim regime is working".
The European Union, Russia and South Korea have welcomed the shift in US-North Korea relations.
South Korea's foreign minister, Kang Kyung Wha, said her government was working with the US in order to ensure a "meaningful meeting with a good outcome".
South Korean President Moon Jae-in said the meeting would be a "historical milestone" that will put the denuclearisation of the Korean Peninsula "really on track".
However, some politicians and experts have voiced scepticism.
Former senior State Department official Evans Revere, who has experience of negotiating with North Korea, warned there could be a disconnect between how the two parties describe denuclearisation.
He said for the US it meant North Korea giving up their weapons, and for North Korea it meant also removing the threat of US forces in South Korea and its nuclear deterrent in the region.