SEOUL (REUTERS) - North Korea responded on Friday (May 25) with measured tones to United States President Donald Trump's decision to call off a historic summit with leader Kim Jong Un scheduled for next month. It said Pyongyang hoped for a "Trump-style solution" to resolve the stand-off over its nuclear weapons programme.

On Thursday, Mr Trump wrote a letter to Mr Kim to announce his withdrawal from what would have been the first-ever meeting between a serving US President and a North Korean leader in Singapore on June 12.

"Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it would be inappropriate, at this time, to have this long-planned meeting," Mr Trump wrote.

Mr Trump's announcement came after repeated threats by North Korea to pull out of the summit over what it saw as confrontational remarks by US officials.

Friday's response by North Korean Vice-Foreign Minister Kim Kye Gwan was more conciliatory, specifically praising Mr Trump's efforts.

"We had hoped a 'Trump-style solution' would be a wise way to relieve worries from both sides, meet our demands and realistically resolve problems," he said in a Korean language statement carried by state media, without elaborating.

The foreign ministers of the United States and South Korea agreed to continue working towards creating the right conditions for the United States and North Korea to talk, the South's Foreign Ministry said in a statement on Friday.

South Korean Foreign Minister Kang Kyung Wha and US Secretary of State Mike Pompeo held a phone call and made the remarks after the summit was called off, the statement said.

North Korea has sharply criticised suggestions by senior US officials - including Vice-President Mike Pence - that it could share the fate of Libya if it did not swiftly surrender its nuclear arsenal.

Libyan leader Muammar Gaddafi was deposed and murdered by Nato-backed militants after halting his nascent nuclear programme.

Mr Kim Kye Gwan said such criticisms had only been a "protest" against American rhetoric, and that it showed the need for talks with Washington.

"To announce the summit is cancelled was a surprise for us and we couldn't help but feel it was a deep shame," Mr Kim Kye Gwan said, while noting that North Korea remained open to resolving issues with Washington "at any time in any way".

NUCLEAR SITE DECOMMISSIONED

Mr Trump's letter came just after North Korea announced it had completely dismantled its Punggye-ri nuclear test facility "to ensure the transparency of discontinuance of nuclear test".

With Mr Trump saying he is keeping the door open to diplomacy and North Korea apparently still looking to benefit from a thaw with South Korea, such steps could be constrained - or at least tempered - by a mutual desire to keep things from spiralling out of control.

But with a new exchange of super-charged rhetoric driving the United States and North Korea from the negotiating table, there is growing concern that words could be matched with action, including renewed shorter-range missile tests or stepped-up cyber attacks by Pyongyang and increased sanctions or deployment of new military assets by Washington, analysts said.

Mr Trump, in scrapping the June 12 summit in Singapore, sounded a bellicose note, warning Mr Kim of the United States' greater nuclear might, reminiscent of the President's tweet last year asserting that he had a "much bigger" nuclear button than Mr Kim.

Speaking later, Mr Trump said the US military stood ready if Mr Kim were to take any "foolish" action.

Asked if the summit cancellation increased the risk of war, Mr Trump replied: "We'll see what happens."

He said the United States would continue its "maximum pressure" campaign of sanctions to press North Korea to give up its nuclear weapons.

South Korean President Moon Jae In, who worked hard to help set up the summit and urged Mr Trump at a White House meeting on Tuesday not to let a rare opportunity slip away, said he was "perplexed" by the cancellation.

He urged Mr Trump and Mr Kim to talk directly.

Pyongyang had not responded in recent days to queries by the United States as it tried to prepare logistics for a June 12 leaders' summit, Mr Pompeo told a Senate hearing.

Japanese Foreign Minister Taro Kono said Tokyo understands Mr Trump's decision to cancel the Singapore summit, Kyodo News reported.

"It's meaningless to have talks that don't achieve results," Mr Kono told reporters on a visit to Mexico City, the news agency said.

Japanese Defence Minister Itsunori Onodera also played down the significance of the cancelled meeting.

"The important thing is not the US-North Korea meeting itself, but that the meeting becomes an opportunity to move forward in the issues of denuclearisation and abductions," he told reporters in Toyko.

The news of the cancelled summit prompted a deluge of derisory comments on Twitter, including many about the now discounted commemorative coin pre-minted for the occasion.

The "President Trump United States and Korea Summit" coin, which was the "deal of the day" at the White House Gift Shop on Thursday, shows gold embossed images of Mr Trump and Mr Kim facing each other with a montage of their countries' flags in the background.

Mr Kim's title is designated as "Supreme Leader".