North Korea said Friday it remains open to talking with the United States to work toward peace and stability, in a markedly restrained response to U.S. President Donald Trump's cancellation of what would have been a historic summit with its leader Kim Jong Un.

"We would like to make known to the U.S. side once again that we have the intent to sit with the U.S. side to solve problem regardless of ways at any time," Kim Kye Gwan, a vice foreign minister, said in a statement carried by the country's official media.

The diplomat, who is North Korea's long-serving point man on nuclear issues, made the statement hours after Trump announced he had decided to call off the scheduled June 12 summit in Singapore, citing recent hostile remarks by Pyongyang.

[Korea Summit Press Pool]

"We remain unchanged in our goal and will to do everything we could for peace and stability of the Korean Peninsula and humankind," the official said in the statement, carried by the Korean Central News Agency, adding, "We, broad-minded and open all the time, have the willingness to offer the U.S. side time and opportunity."

A day after Trump cautioned that the U.S. military is prepared to respond to any "foolish or reckless acts" by North Korea, the diplomat made the swift response, indicating that the country still wants to seek security guarantees from Washington by holding a summit.

North Korea recently warned that it could cancel the summit, lambasting ongoing joint military drills by South Korea and the United States, as well as Washington's call for Pyongyang to unilaterally abandon its nuclear weapons.

On Thursday, Choe Son Hui, another North Korean official in charge of negotiations with the United States, criticized comments by U.S. Vice President Mike Pence about how Pyongyang should proceed with denuclearization as "ignorant" and "stupid."

In an interview broadcast Monday, Pence said North Korea could end up like Libya if Kim "doesn't make a deal," conjuring up the fate that former Libyan leader Muammar Gaddafi met some time after agreeing to abandon his nascent nuclear weapons program in the early 2000s.

Gaddafi was overthrown and killed after a North Atlantic Treaty Organization-led coalition intervened in support of an uprising in the North African country in 2011.

Trump said Choe's remarks were based on "tremendous anger and open hostility."

"Our military -- which is by far the most powerful anywhere in the world and has been greatly enhanced recently, as you know -- is ready if necessary," Trump also said in remarks at the White House, in reference to a possible resumption of nuclear and missile tests, or other provocations, by Pyongyang.

U.S. officials have proposed that North Korea agree to a "Libya-style" denuclearization process, in which Pyongyang first gives up all its nuclear weapons before receiving any benefits.

Kim was believed to be concerned that even if Pyongyang gives up all its nuclear weapons in return for U.S. security assurances, Washington could break its promise, attempting to invade North Korea or overthrow the government.

Trump's letter to Kim about canceling their summit was made public just after North Korea said it had dismantled its only known nuclear test site as promised, amid doubts that Pyongyang would really implement concrete steps toward denuclearization.

North Korea said the demolition marks "important progress" toward "nuclear disarmament," but Pyongyang has yet to pledge to give up its nuclear weapons despite Trump's request.

On Friday, foreign media such as CNN, invited by North Korea to observe the demolition of the Punggye-ri test site, and Pyongyang disclosed images showing smoke rising at the mouth of a tunnel and wooden buildings.

At his summit with South Korean President Moon Jae In on April 27, Kim promised to shut down the nuclear test site and invite experts and media from overseas to witness its dismantlement to ensure transparency.

North Korea, however, did not invite experts such as officials from the International Atomic Energy Agency, raising concern that the actual condition of the test site will not be learned.