Donald Trump has released a copy of a letter from Kim Jong-un, the North Korean leader, praising their meeting as the start of a "meaningful journey".
The US president called it a "very nice note from Chairman Kim" and said "great progress is being made".
In his letter, which was written 24 days after the June 12 summit in Singapore, Kim addressed Mr Trump as "Your Excellency Mr President".
He wrote: "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.
"I sincerely 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 US, will surely come to fruition."
Kim said he had "invariable trust and confidence" in Mr Trump and that there had been "epochal progress" in relations between the two countries.