Pompeo has insisted that a raft of tough economic sanctions imposed on North Korea would remain in place until "final, fully verified denuclearization" occurs.
North Korea did not take kindly to the content of Pompeo's visit, which covered what the US definition of denuclearization is and what would be needed for sanctions relief.
What was in Kim's letter?
Trump tweeted accompanying a Korean and English version of the note from Kim.
He expressed his hope that "the invariable trust and confidence" the president has in him will be "further strengthened in the future process of taking practical actions". He tweeted after the summit that "there is no longer a nuclear threat from North Korea", and he has praised the "great success" during campaign rallies. He did not elaborate. Trump has already unilaterally suspended U.S. -ROK military exercises because they are "provocative" (North Korea's description adopted by Trump) and because they are "expensive" (Trump's words adopted by Trump).
Last week, North Korea accused the USA of using a "gangster-like" tactics to push it towards nuclear disarmament after a fresh round of high-level talks.
That was the day Secretary of State Mike Pompeo arrived for two days of meetings with top North Korean officials, which ended on a sour note after Pyongyang blasted the US side for issuing a "unilateral and gangster-like demand for denuclearization". Great progress being made!
The date of Mr Kim's letter suggests it may have been sent before Mr Pompeo's visit. He promised that working-level meetings would follow on repatriation of remains and that talks would continue on decommissioning of the missile engine test site.More news: Dozens injured after storm hits RV park in North Dakota
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It had been expected on Thursday at the inter-Korean truce village of Panmunjom.
A scheduled meeting between North Korean and U.S. officials on Thursday in the demilitarised zone between the two Koreas to discuss the return of the remains was postponed to Sunday.
President Donald Trump held a first meeting with Kim in Singapore on June 11 of this year to discuss denuclearization of the Korean peninsula.
Trump told a crowd of supporters a week later that the remains of 200 Americans "have been sent back". The two countries have resisted toughening sanctions on North Korea.
According to the Pentagon, North Korean officials have indicated in the past that they have the remains of as many as 200 United States troops.
"We were ready", the official said.
An estimated 30,000 U.S. soldiers died in the 1950-53 Korean war.
The report claims that North Korea could have imported up to 1.3 million barrels of refined supplies, which were obtained through ship-to-ship transfers at least 89 times. It does not, however, give any mention to the end of North Korea's nuclear program, nor the end of the country's regular human rights abuses.