The “deal of the day” in relation to the US and North Korea was widely publicised by the White House. It was not a forecast of a vital breakthrough in the summit between Donald Trump and Kim Jong-un, however, but a coin produced to commemorate the historic moment.

The “President Trump United States and Korea Summit Coin” was put on sale at the White House gift shop just a few hours before the US president pulled out of the summit – a small example of the overall confusion which had marked the US administration’s position over the talks with Pyongyang.

The price dropped with news of the cancellation, from $34.96 to $26.30 and then $19.95 – relatively cheap for what is becoming a collectors’ item, albeit not for the reasons Mr Trump, who apparently believes he would win the Nobel Peace Prize for achieving a nuclear deal, would have wanted.

North Korea’s reaction to the US president’s decision was to express “great regret”, stressing that it was open to talks “at any time” and would wait “to offer the US side time and opportunity”.

There was massaging of Mr Trump’s ego with praise for his “bold” original decision to hold the negotiations and the ingratiating “we even inwardly hoped that what is called ‘Trump formula’ would be a wise way of settling the issue”.

The fact remains that Kim Jong-un has won on the public relations front in this round. The US will be widely viewed as the side which is throwing away the opportunity to settle a combustible problem, while the North Koreans take a reasonable position.

And Mr Trump’s words, threatening military action while at the same time saying “nobody should be anxious” and that he was open to future negotiations will, not for the first time, raise questions about the coherence of his strategy.

The manner in which the US president pulled out of the summit, which was due to be held in Singapore next month, has created rifts with allies.

The leader of South Korea, who had been instrumental in getting Kim Jong-un to the negotiating table, while agreeing to let Mr Trump take the credit for it, was not informed about the decision.

President Moon Jae-in said he was “very perplexed” by what had happened and it was “very regrettable” that the meeting was not going ahead, adding “denuclearisation of the Korean peninsula and the establishment of permanent peace are historic tasks that can neither be abandoned nor delayed”.

The US president had blindsided the Japanese when he first agreed to meet Kim Jong-un, breaking a pledge of consultation he is supposed to have made to Prime Minister Shinzo Abe.

Tokyo was kept in the dark this time around as well. Foreign Minister Taro Kono was on a visit to Washington, but he, too, wasn’t told about the decision beforehand.

Mr Abe is in Russia to meet Vladimir Putin, part of a deepening of relationships which has come about partly in reaction to the unpredictability of the Trump administration’s foreign policy.

He said “It is unfortunate that the summit has been cancelled but we fully respect and support President Trump’s decision.”

Donald Trump says North Korea summit 'could still happen'

China is the one country whose support the US needs in tackling North Korea and there has been acknowledgement from American officials that Beijing’s stricter enforcement of sanctions has been a major factor in making Pyongyang negotiate.

Yet Mr Trump chose to lay blame on China for the summit not taking place, claiming it may have instigated Pyongyang to be less cooperative.

“There was a difference when Kim Jong-un left China for the second time, I can’t say I am happy about it,” he complained.

In reality the prospect of the Singapore meeting being a success began to disappear when Mr Trump’s new national security adviser, John Bolton, declared that Kim Jong-un must take the “Libya model” – one under which Muammar Gaddafi gave up his nuclear programme only to be overthrown a few years later by US and Nato bombing, hunted down and lynched in the street.

The White House distanced itself from Mr Bolton’s remarks. But Mr Trump, who appeared not to know that the term “Libya model” was used for Gaddafi disarmament, and not the bombing by the West which followed, declared that devastating military action was indeed what North Korea would face unless it came to an agreement.

There was also a third evocation of Libya by Vice President Mike Pence who said that North Korea would “end like the Libya model ended” if Mr Kim backed out of the meeting. Asked if that was a threat, Mr Pence responded: “I think it’s more a fact.”

All this would have looked alarming from Pyongyang and there is likely to have been further consternation when Mr Trump’s new secretary of state and national security adviser contradicted each other about what may happen in North Korea in the future.

Secretary of State Mike Pompeo, who had travelled to North Korea to arrange the summit, said in a TV interview that the US would help rebuild the country’s shattered economy after a lasting agreement, only for Mr Bolton to slap it down with: “I wouldn’t look for economic aid from us.”

North Korea reacted by calling Mr Bolton “repugnant” and Mr Pence “stupid” and a “dummy”. It also stated that a “nuclear to nuclear” showdown was a possibility if talks fail, a threat Mr Bolton was quick to bring to Mr Trump’s attention.

Cancelling the meeting, the US president pointed to Pyongyang’s “tremendous anger and open hostility” and boasted of America’s “massive and powerful” nuclear capabilities.

Backdoor channels will be kept open for talks, say both Washington and Pyongyang, and the South Koreans have stated they will help rebuild contacts.