Trump yesterday cancelled his proposed summit meeting with North Korean leader Kim Jong-un on June 12 in Singapore and blamed Pyongyang's "tremendous anger" and "open hostility" for his dramatic decision.
His announcement came hours after North Korea carried out what it said is the demolition of its nuclear test site yesterday.
Reacting to Trump's letter, North Korea today said it was still willing to talk to the US though the President has cancelled the summit.
"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.
"We again state to the US our willingness to sit face-to-face at any time in any form to resolve the problem," Kim was quoted as saying by the state-run KCNA news agency.
Trump in his first reaction to the North Korean statement welcomed Pyongyang's reaction.
"Very good news to receive the warm and productive statement from North Korea," Trump said in an early morning tweet.
"We will soon see where it will lead, hopefully to long and enduring prosperity and peace. Only time (and talent) will tell!" he said in another tweet.
Though he cancelled June 12 summit, however, kept the door open for future talks with Kim.
"If you change your mind having to do with this most important summit, please do not hesitate to call me or write. The world, and North Korea in particular, has lost a great opportunity for lasting peace and great prosperity and wealth. This missed opportunity is a truly sad moment in history," Trump had said in his letter to the North Korean leader.
Washington has made it clear it wants to see the "complete, verifiable and irreversible denuclearisation" of North Korea. But Pyongyang has vowed it will never give up its nuclear deterrence until it feels safe from what it terms US aggression.