Seoul, South Korea (CNN) North Korea says Kim Jong Un is still willing to meet Donald Trump "at any time," despite the US President's abrupt cancellation of what would have been a historic summit between the two leaders, scheduled for June 12.

Kim Kye Gwan, a top official at North Korea's Foreign Ministry, said Trump's decision to cancel the talks ran counter to the global community's wishes for peace on the Korean Peninsula.

"We would like to make known to the US side once again that we have the intent to sit with the US side to solve problem(s) regardless of ways at any time," said Kim in comments published Friday by the country's state-run news agency KCNA.

Kim said President Trump's decision is "not consistent with the desire of humankind for peace and stability in the world, to say nothing of those in the Korean Peninsula."

Trump canceled the summit Thursday in a letter addressed to Kim Jong Un, citing recent hostile comments from top North Korean officials and concern over Pyongyang's commitment to giving up its nuclear weapons. Trump said it would be "inappropriate" to have the summit given his worries.

The final straw, US officials said, was a statement on Thursday from North Korea's Foreign Ministry calling US Vice President Mike Pence a "political dummy" and hinting that Pyongyang was ready for a "nuclear showdown" should diplomacy fail.

Trump's administration claimed there had been hiccups behind the scenes. In a background briefing a senior White House official said the North Koreans had failed to turn up to a meeting with a White House official in Singapore to talk planning and logistics. "The North Koreans didn't tell us anything. They simply stood us up," the official said.

But despite Trump's abrupt cancellation, he appeared to leave the door open for talks to resume at some point, telling reporters Thursday that "if and when Kim Jong Un chooses to engage in constructive dialogue and actions, I am waiting."

Next steps

With the summit now off, US allies and other stakeholders in the region were left scrambling to figure out their next steps.

South Korean President Moon Jae-in, who acted as a middleman between Trump and Kim, called an emergency meeting in the middle of the night after the White House went public with the cancellation.

Moon's Foreign Minister Kang Kyung-wha spoke with US Secretary of State Mike Pompeo early Friday about President Trump's sudden decision and the next steps for Washington and Seoul, two longtime allies. According to a South Korean statement, they said both sides should "devote effort to save the dialogue opportunity."

The United States' other key partner in the region, Japan, was always more skeptical about what could be achieved at the summit. Prime Minister Shinzo Abe is among the more hawkish leaders in Asia when it comes to North Korea. His chief spokesman said Friday that the US and its allies must continue the campaign to isolate North Korea diplomatically and pressure it using economic sanctions.

China has always been key to that strategy, as it accounts for nearly 90% of North Korea's imports, at least on the record.

China's Foreign Ministry said Friday it hoped the United States and North Korea would "maintain patience, release good will and move in the same direction" to push the denuclearization process forward.

"The Chinese government's position on this issue is consistent and clear. We think, as the two directly involved parties, North Korea and the US holding a summit plays a key role in promoting denuclearization on the peninsula," said ministry spokesman Lu Kang.

He said China was playing a "positive and constructive role" regarding the resolution of the nuclear issue. "We don't have any ulterior motives," he added.

Some experts say that China may be less willing to enforce tough measures if it believes that Washington isn't committed to pursuing diplomacy alongside sanctions.

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

'Bold decision'

Analysts said North Korea's response to Trump's letter was fairly measured, especially when compared to Pyongyang's usual bombastic rhetoric.

The two countries have traded insults in the past with Trump calling Kim "little rocket man" and a "sick puppy," and North Korean state media referring to the US President as a "dotard." But in recent months, as relations improved, they've moderated their language with respect to their leaders.

Even after the talks were canceled, North Korean Foreign Ministry official Kim Kye Gwan complimented the US President on his willingness to take a risk and meet with Kim Jong Un.

"We have inwardly highly appreciated President Trump for having made the bold decision, which any other US presidents dared not, and made efforts for such a crucial event as the summit," Kim Kye Gwan said in Friday's statement.

"We remain unchanged in our goal and will to do everything we could for peace and stability of the Korean Peninsula and humankind, and we, broadminded and open all the time, have the willingness to offer the US side time and opportunity."

Nuclear sites 'destroyed'

Hours before Trump canceled the summit, Pyongyang held a ceremonial dismantlement of its Punggye-ri nuclear test site , which it has billed as an example of its "commitment to building a nuclear-free, peaceful world," as one North Korean official at the site put it.

Kim Jong Un announced last month that the site would be shuttered, as it has served its purpose and North Korea's nuclear weapons program was advanced enough that it no longer needed to set off nukes undergorund.

International journalists, including a crew from CNN, watched as a series of explosions appeared to destroy three of four tunnels at the site -- the North Koreans said the fourth tunnel, used for the country's first nuclear test in 2006, had already been destroyed.

Though there were no nuclear or nonproliferation experts on the trip to verify if the site was actually rendered unusable -- something the White House said that North Koreans promised -- the decision to invite foreigners to one of the country's most secretive sites holds symbolic importance.

The CNN team spent about nine hours at the site , during which it was briefed by the deputy director of North Korea's Nuclear Weapons Institute -- who declined to give his name to the visiting journalists -- and was allowed to inspect the tunnels.

"The dismantling of the nuclear test ground conducted with high level of transparency has clearly attested once again to the proactive and peace-loving efforts of the government of the DPRK (Democratic People's Republic of Korea)," the official from North Korea's nuclear weapons institute said.

China's Foreign Ministry on Friday welcomed the apparent destruction of the site as an important step toward denuclearization that should be recognized and encouraged.

Photos: North Korea blows up tunnels at nuclear test site Detonation of entrance to tunnel 2 and the observation building next to it. Photos by CNN Beijing bureau chief Tim Schwarz Hide Caption 1 of 13 Photos: North Korea blows up tunnels at nuclear test site The deputy director of the North Korean Nuclear Weapons Institute briefs reporters before the demolitions begin. Hide Caption 2 of 13 Photos: North Korea blows up tunnels at nuclear test site A close-up of a soldier standing guard in front of an observation building at tunnel 2. Hide Caption 3 of 13 Photos: North Korea blows up tunnels at nuclear test site A soldier stands guard in front of the soon to be demolished observation building of tunnel 2. Hide Caption 4 of 13 Photos: North Korea blows up tunnels at nuclear test site Detonation of entrance to tunnel 2 and the observation building next to it. Hide Caption 5 of 13 Photos: North Korea blows up tunnels at nuclear test site Detonation of entrance to tunnel 2 and the observation building next to it. Hide Caption 6 of 13 Photos: North Korea blows up tunnels at nuclear test site Journalists are taken to inspect the aftermath of the explosion at the mouth of tunnel 2. Hide Caption 7 of 13 Photos: North Korea blows up tunnels at nuclear test site Journalists take photographs at the entrance to tunnel 3. Hide Caption 8 of 13 Photos: North Korea blows up tunnels at nuclear test site A soldier stands at the entrance to tunnel 3. Hide Caption 9 of 13 Photos: North Korea blows up tunnels at nuclear test site A view inside tunnel 3. Hide Caption 10 of 13 Photos: North Korea blows up tunnels at nuclear test site The entrance to tunnel 4, an unused tunnel that North Koreans say was ready to conduct advanced nuclear weapons tests. Hide Caption 11 of 13 Photos: North Korea blows up tunnels at nuclear test site A close-up of explosives rigged at the entrance to tunnel 4, an unused tunnel. Hide Caption 12 of 13 Photos: North Korea blows up tunnels at nuclear test site Explosive charges were placed back as far as the eye could see in tunnel 4. Hide Caption 13 of 13

High hopes

There were high hopes for what would have been a historic summit between the two leaders after Trump unexpectedly accepted an offer for face-to-face talks that Kim made in early March.

It would have been the first encounter between a sitting US President and North Korean leader but plans began to unravel after North Korea objected to joint US-South Korean military drills and comments from senior members of the Trump administration.

After a successful summit between Moon and Kim, a pledge from the young North Korean leader to shutter his nuclear test site and refrain from launching missiles, and the decision to free three Americans held in North Korea, things seemed to be proceeding well until Pyongyang's shift in tone last week.

some analysts believe that Pyongyang's recent provocative language wasn't meant to push Washington to cancel the meeting, but rather to voice their displeasure after Trump's national security adviser, brought up the case of Libya when discussing North Korea. Butsome analysts believe that Pyongyang's recent provocative language wasn't meant to push Washington to cancel the meeting, but rather to voice their displeasure after Vice President Pence and John Bolton Trump's national security adviser, brought up the case of Libya when discussing North Korea.

Former Libyan leader Moammar Gadhafi agreed to give up his nuclear weapons but less than a decade later was ousted from power and killed with the help of NATO-backed forces.

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North Korea has long cited Libya as an example to show why it needs nuclear weapons to deter the United States.

"They were trying to signal to Washington that they were very displeased about all this talk about Libya, which is obviously a nightmare scenario for North Korea, said Sue Mi Terry, a senior fellow at the Center for Strategic and International Studies and former CIA analyst.

"I think that message didn't come across to Washington ... the North Koreans were trying to send a signal and something was lost in translation."