"We have inwardly highly appreciated President Trump for having made the bold decision, which any other USA presidents dared not, and made efforts for such a crucial event as the summit", Kim said in a statement carried by state media.
In Pyongyang, North Korean Vice Foreign Minister Kim Kye-gwan said North Korea's recent criticisms of certain United States officials had been a reaction to unbridled American rhetoric and that the current antagonism showed "the urgent necessity" for the summit.
The Independent's Samuel Osborne and Andrew Buncombe remark that through this historic meeting "Trump, a natural showman, wanted to pull off something no other U.S. president had done; no sitting United States president has met with either of the three members of the Kim dynasty that have ruled North Korea since its creation in 1948". Trump, in his letter to Kim Jong Un, did the same.
North Korea had sharply criticised suggestions by Trump's national security adviser, John Bolton, and Vice President Mike Pence that it could share the fate of Libya if it did not swiftly surrender its nuclear arsenal. Libyan leader Muammar Gaddafi was deposed and murdered by NATO-backed militants after halting his nascent nuclear program.
The decision blindsided treaty ally South Korea, which until now had brokered a remarkable detente between Washington and Pyongyang.
"Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate, at this time, to have this long-planned meeting", read Trump's letter to Kim. He added that North Korea "inwardly highly appreciated" Trump for agreeing to the summit, and hoped the "Trump formula" would help lead to a deal between the adversaries. White House Press Secretary Sarah Huckabee Sanders also said: "This is the President Trump model".
Trump called off the unprecedented meeting, scheduled for June 12 in Singapore, after months of diplomatic progress had silenced bellicose rhetoric from the two sides and eased fears of a return to war.
South Korean President Moon Jae-in, who leapt on the Pyeongchang Winter Olympics as an opportunity to broach a detente with his prickly neighbour, is unlikely to abandon the process now - even at the cost of a deterioration of his country's United States alliance. However, Trump had suggested in recent days that Kim's more defiant tone followed a meeting with Chinese President Xi Jinping.
Women attend a protest against U.S. President Donald Trump near U.S. embassy in Seoul, South Korea, May 25, 2018.
The move may have shocked the world but as the BBC's Heather Chen and Minji Lee of BBC News Korean write, it's an even bigger setback for the people at the heart of it: North and South Koreans.
Just hours before the summit was canceled, North Korea claimed it had made good on its promise to destroy the Punggye-ri facility - and its broader commitment to peace.
For a while, this effort appeared to be working.
North Korea said on Friday that it is willing to talk to the United States "at any time." . Hours after releasing his cancellation letter on Thursday, the president declared, "I really believe Kim Jong Un wants to do what's right".
Japanese Defense Minister Itsunori Onodera told reporters Friday that his agency would "continue monitoring and surveillance activities against North Korea", according to the Asahi newspaper.
"I don't think Trump is doing the right thing if he wants to win the Nobel Peace Prize".
This was after President Donald Trump abruptly cancelled a summit, prompting China to urge both sides to show restraint as a pall of uncertainty settled over the turbulent Korean peninsula once more. "These are the North Koreans".
However it would not be surprising for Beijing to allow increased informal trade with Pyongyang, given Kim's improved relationship with Xi, and the unilateral good faith measures taken by the North that include the destruction of it nuclear test site on Thursday, the release of US prisoners, and the continued suspension of further nuclear and missile tests. Moon may lose the driver's seat for good if Pyongyang reverts to provocative weapons tests, which would bring back USA talk of using military force against the North.
Jeremy Corbyn has called for a united Ireland
He will also talk about the issues around Brexit, with the Irish border and customs arrangements now dividing the Government. They added that Mr Corbyn "respects the Belfast Agreement and the process".