Trump has already spoken to Moon by phone, in a 20-minute call following the United States president's historic meeting with North Korean leader Kim Jong Un on Tuesday, which saw a pledge from both leaders to work towards the complete denuclearisation of the Korean peninsula.
Even as Pompeo staunchly defended the summit results, he was less exuberant than Trump, who tweeted on his return to the US on Monday morning: "Just landed - a long trip, but everybody can now feel much safer than the day I took office".
Trump and Kim signed a document on Tuesday stating that Pyongyang would work toward "complete denuclearization of the Korean Peninsula".
Trump also drew criticism for announcing he was ending joint "war games" with South Korea, embracing the frequent North Korean criticism that the exercises are "very provocative".
At times, the video speaks to Kim directly, suggesting he could make a choice that would open North Korea up to new investment and step into a starring role in a moment in history with Trump. "No longer - sleep well tonight!" the President wrote. He met for almost an hour with Gen. Vincent Brooks, commander of U.S. Forces Korea, at the air base before heading by motorcade to Seoul.
Kim's vows to denuclearize were reported by state media Wednesday within that context - that Pyongyang would respond to easing of what it sees as the hostile usa policy with commensurate but gradual moves toward "the complete denuclearization of the Korean Peninsula".
"The nuclear threat from North Korea today is exactly the same as what it was several weeks ago", Einhorn said.
The Korean Central News Agency (KCNA) reported that Kim and Trump agreed that "it is important to abide by the principle of step-by-step and simultaneous action in achieving peace, stability and denuclearization of the Korean Peninsula". But at his post-summit news conference, the USA president described them as "very provocative". Even in cases where the US president has studied his briefing materials, unlike Trump, having others present can prevent a situation where the two nations disagree about what promises were made.
"I have no idea" whether Trump secured anything of substance, Senator Corker, the retiring chairman of the Senate Foreign Relations Committee said. The US had sided with South Korea in the conflict.
Pompeo was in Seoul on Wednesday to brief South Korean officials on the summit.
Donald Trump and Kim Jong-un were returning to their respective strongholds following the talks _ but to far different receptions. -South Korea military exercises along the demilitarized zone separating the two Koreas, a tangible concession that drew criticism from a number of lawmakers back home.
When Singaporean Prime Minister Lee Hsien Loong visited the worldwide media center for the summit at F1 Pit Building on Sunday, he said it will cost the city state "around 20 million Singaporean dollars" (W16.1 billion, US$1=W1,078) to host the "historic summit".
Beijing immediately hinted that the United Nations could consider lifting the punishing sanctions on North Korea that Trump credits with bringing Kim to the table.
The South Korean president responded positively to the summit, praising the "courage and determination" of both leaders.
The Pentagon said on Tuesday that it was consulting with the White House and others, but was silent on whether the August exercise would proceed.
Some analysts are likely to see the comments as part of a worrying trend since North Korea showed no public sign at the summit or since that it is now willing to implement the complete, irreversible and verifiable destruction of its nuclear programs.