"A very nice note from Chairman Kim of North Korea," Trump tweeted alongside a copy of the letter dated July 6 -- the day that US Secretary of State Mike Pompeo landed in Pyongyang for what turned out to be difficult talks with Kim's regime.

"Great progress being made!" Trump added in his tweet.

In the letter Kim describes his June 12 summit with Trump in Singapore, and the resulting joint statement agreed by both sides, as the "start of a meaningful journey."

"I firmly believe that the strong will, sincere efforts and unique approach of myself and Your Excellency Mr. President aimed at opening up a new future between the DPRK and the U.S. will sure surely come to fruition," Kim writes.

"I deeply appreciate the energetic and extraordinary efforts made by Your Excellency Mr. President for the improvement of relations between the two countries and the faithful implementation of the joint statement," he adds.

The North Korean leader also voices hope that "the invariable trust and confidence in Your Excellency Mr. President will be further strengthened in the future process of taking practical actions."

Pompeo traveled to Pyongyang for two days last week in a bid to flesh out denuclearization commitments made during last month's historic summit between Trump and Kim.

North Korea has long trumpeted a denuclearization goal, but one that it sees as a lengthy process of undefined multilateral disarmament on the entire Korean peninsula, rather than a unilateral dismantlement of its nuclear arsenal.

Speaking afterwards in Tokyo, Pompeo insisted the talks were making progress and were being conducted in "good faith."

But in stark contrast, Pyongyang's take was overwhelmingly negative, with the North warning that the future of the peace process was being jeopardized by overbearing US demands for its unilateral nuclear disarmament.