US President Donald Trump threatened Kim Jong-un with military action - AFP

North Korea said on Friday it was still open to talks with the US despite Donald Trump's threat of military action after cancelling their June 12 summit in Singapore.

Pyongyang described the US president's decision to pull the plug on the highly anticipated meeting as "extremely regrettable".

"The abrupt announcement of the cancellation of the meeting is unexpected for us and we cannot but find it extremely regrettable," Kim Kye Gwan, North Korea's First Vice Foreign Minister, said in a statement carried by the state-run KCNA news agency.

"We again state to the US our willingness to sit face-to-face at any time in any form to resolve the problem," Mr Kim added.

The US president said on Thursday the American military was “ready if necessary” to react with its allies should North Korea take any “foolish or reckless acts”.

North Korean leader Kim Jong Un inspects the completed railway that connects Koam and Dapchon, in this undated photo released by North Korea's Korean Central News Agency Credit: Reuters

He softened his tone on Friday morning after North Korea's response, tweeting: "Very good news to receive the warm and productive statement from North Korea. We will soon see where it will lead, hopefully to long and enduring prosperity and peace. Only time (and talent) will tell!"

On Thursday Mr Trump shocked many as he announced he had formally scrapped the summit through a letter released by the White House.

The US president wrote to Kim: “We were informed that the meeting was requested by North Korea, but that to us is totally irrelevant. I was very much looking 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 this long-planned meeting.”

Mr Trump said “this missed opportunity is a truly sad moment in history” and appeared open to the talks being rearranged, saying: “If you change your mind having to do with this most important summit, please do not hesitate to call me or write.”

Sadly, I was forced to cancel the Summit Meeting in Singapore with Kim Jung Un. pic.twitter.com/qEoi9ymUEz — Donald J. Trump (@realDonaldTrump) May 24, 2018

But the US president also issued a clear threat: “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.”

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Mr Trump later said he had talked to James Mattis, the US defence secretary, and the US joint chiefs of staff, adding that “our military… is ready if necessary”.

South Korea's Unification Minister said on Friday that Seoul would press ahead with improving ties with North Korea.

"Our government will do its part in carrying out the Panmunjom Declaration," Unification Minister Cho Myoung-gyon told reporters according to Yonhap, referring to the landmark agreement to bolster ties and push towards denuclearisation signed last month by Kim and South Korean President Moon Jae-in.

"It appears that (the North) remains sincere in implementing the agreement and making efforts on denuclearisation and peace building," he added.

The latest twist in the diplomatic dance on the Korean peninsula came on the same day North Korea followed through on a pledge to blow up tunnels at its nuclear test site.

North Korea has conducted all six of its nuclear tests at the Punggye-ri site, which consists of tunnels dug beneath Mount Mantap in the northeast of the country.

A small group of international media selected by North Korea witnessed the demolition, which Pyongyang says is proof of its commitment to end nuclear testing.

The destruction of the site began at about 11 a.m. with the blowing up and collapsing of a tunnel and an observation post.

North Korea's state-run news agency KCNA reported there was no leak of radioactive materials or any adverse impact on the surrounding ecological environment.

"Dismantling the nuclear test ground was done in such a way as to make all the tunnels of the test ground collapse by explosion and completely close the tunnel entrances, and at the same time, explode some guard facilities and observation posts on the site," KCNA reported.