"The world and North Korea has lost a tremendous opportunity for lasting peace and great prosperity and wealth", Trump wrote.
He added: "This missed opportunity is a truly sad moment in history".
However, Trump said he had spoken to South Korea and Japan and they were ready "if foolish or reckless acts are taken by North Korea" and willing to shoulder the financial cost of any U.S. military operations.
Analysts fear a resumption in hostilities on the Korean peninsula, with renewed missile tests and cyber attacks by Pyongyang, and stepped-up sanctions by Washington.
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 USA president had done; no sitting USA president has met with either of the three members of the Kim dynasty that have ruled North Korea since its creation in 1948".
Cheshire said Mr Kim was reportedly "unruffled" and the North Koreans had responded to Mr Trump's move with "equanimity".
But even as North Korea carried out the destruction of the nuclear test site, North Korea and Washington remained poles apart over the pace of any road to denuclearisation, with North Korea wanting a staged approach and the USA pushing for complete denuclearisation before any concessions were made. -South Korea military exercises, which he'd previously said were fine. Putin said of Trump's cancellation announcement, "In Russia we took this news with regret".
"We have got some, possibly some good news on the Korea summit, where it may, if our diplomats can pull it off, may have it back on even", Mattis said.
"We are in a boxer stance, we are ready to respond", Lieutenant General Kenneth McKenzie, director of the USA military's Joint Staff, told reporters.
"Moon sees this as his mission", Lee said. We're talking to them [North Korea] now.
However, Trump's decision hasn't come as a complete shock for those who have been following-up the constant back-and-forth from both sides in the run-up to the June meeting.
On oil markets, both main contracts extended Thursday's more than one percent losses after Russian Federation said an agreement with OPEC to cap production - which has provided support to prices in recent years - could be up for revision at a meeting next month.
Trump had called on Pyongyang to abandon its nuclear weapons programme and arsenal ahead of the summit.
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Following the publication of the documents, Trump Jr. said they showed that he " answered every question asked " by the committee. Trump Jr responded "I love it" when first offered the political " dirt " on Clinton, the Democratic presidential nominee.
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"Trump has no interest in peace in our country".
"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.
Cheshire said: "If you think back to a year ago, when he was a pariah, well, he's had all these meetings where he has become more of an worldwide (figure) than a despot back home, especially that historic meeting in the Demilitarised Zone between North and South Korea".
Despite hopes that the dismantlement ceremony will lead to nuclear disarmament, experts remain doubtful of North Korea's true intentions, citing a similar event involving a cooling tower at its Yongbyon nuclear reactor facility in 2008.
US Secretary of State Mike Pompeo told a Senate committee on Thursday the White House had "tried repeatedly" to connect with North Korea in recent days over plans for the Singapore summit, but received no response.
"I don't think it's too late to have a meaningful limit of what they can do", he said of North Korea's nuclear missile program. The US balked at that demand. "I've been studying them for 25 years and in the '90s I thought we had to stop their progress or face it in the future".
That statement referred to Vice President Mike Pence as a "political dummy" for his comments on the North and said it was up to the Americans whether they would "meet us at a meeting room or encounter us at nuclear-to-nuclear showdown".
A spokesperson for Moon's office said on Thursday that South Korea was trying to understand the reason for Trump's abrupt cancellation.
Moon convened an emergency meeting with top security officials after Trump's cancellation.
A sinking feeling had come over her when she loaded up KakaoTalk, South Korea's most popular instant messaging app.
Typically, these talks end with North Korea walking away or taking provocative actions that force the U.S. to walk away. There, former leader Colonel Gaddafi gave up his nascent nuclear programme only for him to be killed by Western-backed rebels a few years later.
"From the beginning to the present, the dealings with North Korea have been sophomoric and without strategic or tactical merit", Hoyer said in a statement.