US President Donald Trump said it was possible a planned summit with North Korea's leader Kim Jong-un could still take place on 12 June as originally planned.

"We're going to see what happens. We're talking to them now," Mr Trump told reporters, one day after he cancelled the highly anticipated meeting.

"It could even be the 12th ... We'd like to do it."

Earlier, he tweeted that North Korea's statement that it was still willing to talk to the US was "very good news".

President Trump yesterday called off the summit, blaming "open hostility" from the North Korean regime and warning Pyongyang against committing any "foolish or reckless acts".

"The abrupt announcement of the cancellation of the meeting is unexpected for us and we cannot but find it extremely regrettable," Kim Kye Gwan, North Korea's First Vice Foreign Minister, said in a statement carried by the state-run KCNA news agency.

"We again state to the US our willingness to sit face-to-face at any time in any form to resolve the problem," Mr Kim added.

In a letter to Mr Kim, Mr Trump announced he would not go ahead with the high-stakes meeting set for 12 June in Singapore, following what the White House called a "trail of broken promises" by the North.

In his statement today, First Vice Foreign Minister Kim said the North Korean leader had been preparing for the summit to go ahead. 

"Our Chairman (Kim Jong-un) had also said a meeting with President Trump would create a good beginning and had been putting effort into prepartions for it," Mr Kim said.

Just before Mr Trump announced the cancellation of the talks, North Korea declared it had "completely" dismantled its nuclear test site, in a carefully choreographed move portrayed as a goodwill gesture ahead of the summit.

However, the chances of success for the unprecedented face-to-face had recently been thrown into doubt.

Yesterday, Pyongyang hardened its rhetoric by attacking US Vice President Mike Pence as "ignorant and stupid".

The broadside appeared to hit a nerve with Mr Trump, leading to him abruptly pulling out of the talks.

"Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate, at this time, to have this long-planned meeting," read Mr Trump's letter to Mr Kim, which was dictated word-for-word by the US leader, according to a senior White House official.