A historic meeting between US President Donald Trump and North Korean leader Kim Jong-un may be back on the cards one day after Mr Trump cancelled the summit with a dramatic personal letter.

“We’ll see what happens. We are talking to them now,” Mr Trump said in Washington on Saturday (Friday local time). “They very much want to do it. We’d like to do it.”

The June 12 meeting between the two countries in Singapore had been months in the making, brokered by an optimistic South Korean President Moon Jae-in.

But the summit fell apart on Thursday after several weeks of hostilities which boiled over after North Korea this week called US Vice President Mike Pence a “political dummy”.

In an expected letter on Thursday, Mr Trump wrote to North Korea’s leader and told him the summit was cancelled.

“I was very much looking forward to being there with you,” Mr Trump wrote. “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.”

“Therefore, 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.”

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

The summit would have been the first face-to-face meeting between a US and North Korean leader.

But United States Secretary of Defense Jim Mattis on Friday echoed Mr Trump’s optimism and said diplomats were “still at work”.

“We have got some, possibly some good news on the Korea summit, where it may, if our diplomats can pull it off, may have it back on even.”

“Our president just sent out a note about that a few moments ago…that is a usual give and take, you know, of trying to put together big summits and stuff. The diplomats are still at work.”

It appears the North Korean government has also had an about-face, on Friday saying it was still willing to talk “at any time in any form” with Mr Trump.

“We express our willingness to sit down face-to-face with the U.S. and resolve issues anytime and in any format,” Vice Foreign Minister Kim Kye Gwan said.

Mr Trump’s letter has been described as extraordinary because he dictated every word instead of having his office prepare it for him.

It struck an incredibly personal note, with Mr Trump expressing his sadness over not being able to meet Mr Kim in person.

It’s understood comments made by Mr Pence comparing North Korea to Libya were particularly provocative.

There, former leader Muammar Gaddafi agreed to give up his nuclear program in exchange for economic assistance but was killed by Western-backed revels several years later.

In an interview this month, Mr Pence threatened North Korea with a similar outcome.

“As the president made clear, this will only end like the Libya model ended if Kim Jong-un doesn’t make a deal,” he said.

Ebony Bowden contributed reporting from New York.