President Donald Trump speaks about the cancelled summit with North Korean leader Kim Jong Un during a bill signing ceremony in the Roosevelt Room of the White House in Washington, D.C., May 24, 2018. Win McNamee/Getty Images

A day after President Donald Trump pulled out of a highly anticipated meeting with North Korean leader Kim Jong Un, Pyongyang said it was still open to the summit.

Trump was set to meet Kim on June 12 in Singapore, which would have been the first summit between a sitting U.S. president and a North Korean leader.

In a release Friday, Kim Kye Gwan, North Korea's First Vice-minister of Foreign affairs, said, “The abrupt announcement of the cancellation of the meeting is unexpected for us and we cannot but find it extremely regrettable.”

Pyongyang said it was willing to hold talks with the United States “at any time” to resolve problems between both nations.

“I would like to conclude that President Trump's statement on the North Korea-US summit is a decision that is not in line with the wishes of the humankind who hope for the peace and stability of the Korean peninsula as well as the world,” the release said.

Kim praised the president for taking the initiative for talks and said, “Trump made a brave decision that no president in the past has made and put efforts to make the summit happen.”

"However, the sudden unilateral cancellation of the summit was an unexpected happening to us and we cannot help but feel very regretful," he said. "Our goal and will to do everything for peace and stability of the Korean Peninsula and the mankind remains unchanged, and we are willing to give time and opportunity to the US, always with a big and open mind."

Trump, on Thursday, called off the historic summit citing the reclusive nation’s "open hostility."

Calling it a "tremendous setback" and a “sad moment in history,” Trump, in a letter to Kim, said, "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 would be inappropriate, at this time, to have this long-planned meeting. Please let this letter serve to represent that the Singapore summit, for the good of both parties, but to the detriment of the world, will not take place."

His decision came shortly after a top North Korean diplomat released a statement calling Vice President Mike Pence a “political dummy” and his comments that likened North Korea to Libya “unbridled and impudent.”

Choe Son Hui, vice minister of foreign affairs, also threatened a military attack on the U.S.

“Whether the U.S. will meet us at a meeting room or encounter us at nuclear-to-nuclear showdown is entirely dependent upon the decision and behavior of the United States. We can also make the U.S. taste an appalling tragedy it has neither experienced nor even imagined up to now,” Choe said in the statement.

Trump, however, said he still has hopes and is looking forward to meeting Kim "some day."

“It’s possible that the existing summit could take place, or a summit at some later date. Nobody should be anxious. We have to get it right. If and when Kim Jong Un chooses to engage in constructive dialogue and actions, I am waiting,” he said.