After his statement on North Korea, Trump answered a few questions from reporters.

"I really believe Kim wants to do what's right," he said.

"The dialogue was good until recently," he added, urging North Korea to "seize the opportunity" to resolve the issue.

The US president also said he knew "what happened" that prompted North Korea to make recent critical remarks, but added that he would not tell this - at least for now.

The US president says he has spoken to Defense Secretary Jim Mattis and allied countries and they are "ready" should North Korea carry out "foolish acts".

He says he is "hopeful" that positive steps can be made but says that if not, "we are more ready than we have ever been before".

A "maximum pressure campaign will continue" on North Korea, says Trump

"We will never compromise the safety and security of the United States of America," he says, adding that he feels "very very strongly about it".

He is now talking about efforts to boost US military strength.

"I hope that Kim Jong-un will ultimately do what is right not only for himself, but perhaps most importantly, what's right for his people who are suffering greatly and needlessly," he says.

Trump is speaking now from the White House

"Based on the recent statements by North Korea I have decided to terminate the planned summit on 12 June.

"Many things can happen and a great opportunity lies ahead potentially," he says.

He adds that this step is a "tremendous setback for North Korea and the world".

UN Secretary General Antonio Guterres has expressed deep disappointment about the cancellation of next month's summit.

He urged all parties to continue their dialogue to try to "find a path to the peaceful and verifiable denuclearisation of the Korean peninsula", Reuters reports.

Image source, White House

Analysis by Anthony Zurcher, BBC Washington

The business letter-writing template kicks in again in the closing paragraph, albeit with somewhat tortured prose. “If you change your mind having to do with this most important summit, please do not hesitate to call me or write”. We have operators standing by!

It finishes on a wistful note. In his tweet announcing the time and place of the now-cancelled summit, the president had said the meeting could be a “very special moment for World Peace”!

His supporters had even broached the idea that he should win a Nobel Prize. Now that prospect appears to have been dashed - and it’s a “sad moment in history”.

Image source, White House

Analysis by Anthony Zurcher, BBC Washington

By the second paragraph, the diplomatic gloves are back on. There’s an emphasis of the recent thaw between the new nations and a hint that suggests the door has not been fully slammed shut.

The two nations had a ”wonderful dialogue”. The president is still looking forward to meeting the North Korean strongman (nuclear apocalypse notwithstanding). And releasing three American prisoners, one of whom had been sentenced to forced labour in a sham trial, was a much-appreciated “beautiful gesture”.

There will certainly be some critics who question whether this is an appropriate place to turn on the charm.

Image source, White House

Analysis by Anthony Zurcher, BBC North America Correspondent

The missive from Donald Trump - addressed to “his excellency”, an unusual title for Kim Jong-Un - begins a bit like a corporate form letter, thanking the North Korean leader for his “time, patience and effort”.

There’s a bit of a passive-aggressive dig at Kim Jong-un - pointing out that he was the one who wanted the meeting, even if that’s “totally irrelevant” - and an emphasis that this was a “long-planned meeting” (the idea was first suggested in March and a date and time set just weeks ago).

The real meat of the letter comes at the end of the paragraph, however, as the president’s pen turns poison.

The North Koreans announced Thursday morning that they had collapsed the tunnels at their nuclear test site, but they accompanied it with threats of nuclear war and a demeaning swipe at Vice-President Mike Pence. Mr Trump has shown time and time again that he won’t abide verbal swipes from the North Koreans.

He responds to their nuclear sabre-rattling with another round of “fire and fury” style language, boasting about the massive and powerful US nuclear arsenal that Donald Trump prays to God will never be used. It’s a return to the rhetoric of last summer, when it appeared the US and North Korea were headed toward a military confrontation. The start of the letter may be diplomat-speak, but this is Mr Trump’s voice coming through.

Image source, AFP/Getty

Who is Kim Jong-un, and how did he leap past the line of succession to become his nation's "supreme leader"?

"He was chosen by his father because he was the meanest and nastiest of the sons," says veteran North Korea observer Bradley Martin.

Read more about the 'King of Pyongyang'

A transcript of the US Senate Foreign Relations Committee room captured senators making jokes about cancelling their flights to Singapore, as they awaited Secretary of State Mike Pompeo to testify.

Secretary of State Mike Pompeo, who has met twice with the North Korean leader in Pyongyang in the past few weeks, explained to a senate committee why he had recommended that the US hold talks with the isolated country.

He also said he was "still optimistic" that talks would eventually take place and said this view was shared by Trump.

“North Korea has a long history of demanding concessions merely to negotiate," Arkansas Senator Tom Cotton said in a statement congratulating Trump for not having "fallen for this ruse".

"I commend the president for seeing through Kim Jong Un’s fraud. As I have long said, our maximum-pressure campaign on North Korea must continue."

Colorado's and Nebraska's Republican senators also praised Trump's decision to cancel.

Image source, Reuters

Trump's announcement that he was cancelling the planned summit with Kim came hours after North Korea said it had dismantled tunnels at its only nuclear test site.

Foreign reporters at the Punggye-ri site in the north-east said they had witnessed a huge blast.

Pyongyang later said the site had been dismantled.

But scientists believe it partially collapsed after the last test in September 2017, rendering it unusable.

North Korea nuclear test tunnels at Punggye-ri 'destroyed'

South Korean President Moon Jae-in met his top security officials after President Trump's decision to cancel the summit, Reuters reports quoting presidential press-secretary Yoon Young-chan.

Mr Trump has now tweeted his letter to Kim Jong-un from his personal Twitter account.

In the tweet itself, he has misspelled the North Korean leader's name, referring to him as "Kim Jung Un".

Secretary of State Mike Pompeo read out Trump's letter to the Senate Foreign Relations Committee at the start of his testimony.

Trump is due to speak at an event to sign a economic growth bill into law.

We do not know if he will be taking questions from reporters.

Some US journalists have expressed surprise that Mr Trump chose to announce his news through a letter rather than a tweet.

He is due to speak at 11:30 local time (15:30 GMT).

Image source, Getty Images

In his letter to Mr Kim, Mr Trump said he had been looking forward to the now-cancelled summit in Singapore on 12 June.

"I was very much looking forward to being there with you. 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 the long-planned meeting," Mr Trump said.

"You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used," he added.

Mr Trump ended his letter by saying Mr Kim should call him if he changed his mind.

"The world, and North Korea in particular, has lost a great opportunity for lasting peace and great prosperity and wealth. This missed opportunity is a truly sad moment in history," he said.

North Korean official Choe Son-hui had earlier said the North would not "beg" for dialogue and warned of a "nuclear showdown" if diplomacy failed.

Analysis by Jonathan Marcus, BBC diplomatic correspondent

The Trump administration insists that North Korea was not responding sufficiently in the summit preparations, raising doubts that the meeting would be able to achieve a positive outcome.

The big question is: what happens now?

Prior to the thaw in relations between North and South Korea that began the process that led to the summit date, wild rhetoric was being exchanged between Pyongyang and Washington raising serious fears of a renewed conflict on the Korean Peninsula.

Will North Korea now resume its long-range ballistic missile testing? Will the war of words be renewed? Or might there be a slim chance of some kind of diplomatic process being maintained?