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 official China Daily said Trump's "cheeky invitation" for Kim to call or write to set up a meeting, meant the letter did not "slam the door shut on talks" in the future.
North Korea hardened its rhetoric toward the US on Thursday, lashing out after remarks by Vice President Mike Pence and the White House national security adviser, John Bolton, that had linked the country with Libya. Libyan leader Muammar Gaddafi was deposed and killed by NATO-backed militants after halting his nascent nuclear program.
After President Trump abruptly called off a June 12 meeting with North Korea's Kim Jong Un to discuss nuclear disarmament, the leader of South Korea is trying to parse the meaning - and the fallout - of the cancellation, as other world leaders express dismay.
Pyongyang had released three American prisoners, agreed to a moratorium on missile tests, quietly accepted a US-South Korean military exercise on its doorstep and even blown up its only atomic weapons testing site.
"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.
But NBC News suggested that Trump sensed the disappointment hiding around the corner and sought to beat the North Koreans to the punch by exiting the summit so quickly he told neither South Korea nor Congress beforehand.
"I think it is worth positively evaluating North Korea showing its willingness to continue the talks with the US, while calmly assessing the current situation", said Kim Yong-hyun, a professor of North Korean studies at Dongguk University in Seoul. White House press secretary Sarah Huckabee Sanders said: "This is the President Trump model".
Trump, in scrapping the June 12 summit in Singapore, sounded a bellicose note, warning Kim of the United States' greater nuclear might, reminiscent of the president's tweet past year asserting that he had a "much bigger" nuclear button than Kim.
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.
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Trump's decision underscores the delicacy of Seoul's intermediary status but also the credibility problems Moon faces over his claim that Kim is genuinely interested in negotiating away his nuclear weapons.
U.S. Secretary of State Mike Pompeo, speaking to a Senate committee on Thursday, would not confirm whether Seoul had been notified. -North Korea talks by persuading Kim to agree to a broad denuclearization goal at the recent inter-Korean summit.
For a while, this effort appeared to be working.
Pyongyang says it remains willing to talk after Mr Trump cancelled, but chances of the summit happening at all now look minimal.
On Friday, North Korea's vice foreign minister said his country's "objective and resolve to do our best for the sake of peace and stability of the Korean Peninsula and all humankind remain unchanged".
Christopher Hill, former USA ambassador to South Korea told CNBC, "Such a gap in expectations on both sides could have been avoided if the U.S. had gotten a better reading of North Korea's intentions, especially since Secretary of State Mike Pompeo had met with North Korean leader Kim Jong Un twice in the past few months".
The Communist Party newspaper, China Daily, ran an editorial Friday calling on the US and North Korea to maintain their "commitment to dialogue" and continue to work toward "an end to hostilities and denuclearization of the Korean Peninsula".
On Friday, Trump called the statement "very good news", adding, "We will soon see where it will lead, hopefully to long and enduring prosperity and peace". "I don't really know that I want to speculate as to why it is they (North Koreans) took the actions, because I don't think we know". It came just hours after the South Korean government issued a statement welcoming the North's dismantling of its nuclear test site, calling it a "meaningful first step" toward denuclearization.
Another user said: "No-one will now believe you, Trump".
But the North's Kim Kye Gwan countered that their angry statements were "just a backlash in response to harsh words from the United States side that has been pushing for a unilateral denuclearisation".