US regional allies Japan and South Korea, as well as North Korea's main ally, China, urged the two countries to salvage the summit on Friday.
The cancellation followed several statements from North Korea threatening to walk, including one Wednesday night that called Vice President Pence a "political dummy" and threatened a "nuclear-to-nuclear showdown" if there's no meeting.
The heavily-amended letter condemned Trump for being repetitive, "pandering" to his audience, inappropriate vocabulary and nonsensical turn of phrase.
"It could even be the 12th", he added.
Protesters with a portrait of US President Donald Trump stage a rally against the United States' policies near the US embassy in Seoul, South Korea, yesterday.
The comments reflected a broadly shared perception inside the White House and State Department that the two leaders still want to get together and there will be a meeting eventually.
Trump also said from the White House that a "maximum pressure campaign" of economic sanctions and diplomatic isolation would continue against North Korea - with which the U.S. is technically still at war - but he added that it was possible the summit could still take place at some point.
After the summit between him and South Korean President Moon Jae-in last month, a poll by the Korean Research Center found 78 per cent of South Koreans said Kim is "trustworthy", a big change in attitudes given his previous infamy here.
"We reiterate to the USA that there is a willingness to sit down at any time, in any way, to solve the problem", a top North Korean official said.
Trump, who spoke to reporters at the White House before heading to the Naval Academy graduation ceremony, stressed that both sides would like the summit to happen.
In his letter to Kim, Trump objected specifically to a statement from senior North Korean diplomat Choe Son-hui.
Trump's cancellation of the summit blindsided treaty ally South Korea, which had brokered the remarkable detente between Washington and Pyongyang.
Trump blamed "open hostility" from Kim's regime for his decision to call off the talks, and warned North Korea against committing any "foolish or reckless acts".
Park tells TIME that although the young generation of South Koreans tended to be skeptical of improvements in inter-Korean relations, Moon and Kim's April 27 meeting had "inspired the young generation to see North Korea differently". "We didn't want to go to a meeting just for the sake of going to a meeting. There had to be something to come out of it".
The question for the Trump administration, though, is whether or not cancelling the summit means the end of engagement and a turn to hawkish moves to force the DPRK to denuclearise, or whether concerted diplomatic efforts will be made to hold lower level talks to iron out substantial issues before a symbolic summit in the future.
"Now that the talks broke down, North Korea will have to take action to bring America back to the table", said Kim Cheol-hong, an office worker outside on a coffee break.
Earlier on Twitter, Trump had noted "very good news to receive the warm and productive statement from North Korea". -North Korea working-level talks this weekend could still take place.
Just hours before Mr Trump cancelled the summit, North Korea said it had carried out its promise to dismantle tunnels at its only nuclear test site.
"Democrats are so obviously rooting against us in our negotiations with North Korea".
At an economic forum in St. Petersburg, Chinese Vice President Wang Qishan said such a summit was necessary to ensure security on the Korean peninsula, which touched on China's core interests.
Indeed, the idea of peace on a peninsula still technically at war has started to feel so real that there's a boom in property sales inside the demilitarized zone (DMZ).
North Korea is not known for its facility with flattery, but Kim's statement appears to have worked in restoring momentum towards a summit meeting. "And a summit is needed to achieve a breakthrough".
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