A senior diplomat of the Democratic People's Republic of Korea said Pyongyang is open to resolving issues with Washington at any time, as US President Donald Trump continued to send mixed messages on Thursday, after abruptly withdrawing from a summit with DPRK's top leader Kim Jong-un.

"We had set in high regards President Trump's efforts, unprecedented by any other president, to create a historic North Korea-US summit," Reuters cited the DPRK Vice-Foreign Minister Kim Kye-gwan as saying in a statement released on Friday by the central news agency KCNA.

"We tell the United States once more that we are open to resolving problems at any time in any way," he said on Friday local time.

Hours after releasing a letter Thursday morning to Kim announcing his decision to call off what would have been a historic meeting in Singapore on June 12, Trump warned a "maximum pressure campaign" would continue against Pyongyang, but that it was possible the summit could still take place.

"If and when Kim Jong-un chooses to engage in constructive dialogue and actions, I am waiting," Trump said. "In the meantime, our very strong sanctions - by far the strongest sanctions ever imposed - and maximum pressure campaign will continue, as it has been continuing."

He added that "a lot of things can happen, including the fact that, perhaps - and would wait - it's possible that the existing summit could take place or a summit at some later date."

Asked on Thursday whether relations with Pyongyang would return to the volatile rhetoric and nuclear threats of the past, US Secretary of State Mike Pompeo, who has met with Kim twice in recent weeks, said, "In some ways it's 'situation normal'. The pressure campaign continues."

Pompeo said he hoped Pyongyang and Washington will be able to resume talks, but the decision was ultimately up to Kim.

"I hope we quickly are able to get back to that place, but ultimately Chairman Kim will have that decision to make for himself," he said at a Senate hearing.

Trump's surprise exit from the talks came shortly after the DPRK dismantled its nuclear test site in front of international journalists, a move that Republic of Korea authorities said was the "first step toward complete denuclearization of the peninsula".

The US complained that international experts and officials were not invited to witness and verify the demolition.

Anthony H. Cordesman of the Center for Strategic and International Studies said Trump's cancellation of the summit with DPRK is a warning as to just how difficult it is to bring any kind of stability to the Korean Peninsula and Northeast Asia.

"It is also a warning that the US cannot focus on the nuclear issue and ICBMs, rather than the overall military balance in the Koreas and the impact that any kind of war fighting can have on the civil population of South Korea and the other states in Northeast Asia," he said in an analysis report on Thursday.

UN Secretary-General Antonio Guterres said on Thursday he was "deeply concerned" by the cancellation of the planned summit and urged those involved in the talks to continue their dialogue to "find a path to the peaceful and verifiable denuclearization of the Korean peninsula".

ROK President Moon Jae-in, who met in Washington with Trump several days ago, said he was "very perplexed" and it was "very regrettable" that the summit won't go ahead as planned.

"Denuclearization of the Korean Peninsula and the establishment of permanent peace are historic tasks that can neither be abandoned nor delayed," Moon said.

Russian President Vladimir Putin, meeting with French counterpart Emmanuel Macron in St. Petersburg, said the DPRK leader "did everything that he had promised in advance, even blowing up the tunnels and shafts of the country's nuclear testing site," the Associated Press reported.

Macron said he hoped Trump's move "was just a glitch in a process that should be continued", according to a Reuters report.

"France is completely disposed to help, but I think it's for the entire international community ... and the United Nations has a particular role to play to work on it," the AP quoted the French leader as saying.