"Secretary Pompeo and the other diplomats who will lead these talks no doubt have a lot of challenging tasks ahead of them, not only in getting North Korea to agree to significant follow-up measures, but in keeping Washington, Seoul and Beijing on the same page as each pursues bilateral engagement with Pyongyang", Daniel Wertz, associate director of the National Committee on North Korea, told Newsweek.
The document the two leaders signed Tuesday did not include details of how and when North Korea would denuclearize, nor did it spell out exactly what "security guarantees" the United States would provide to North Korea. The summit statement provided no details on when Pyongyang would give up its nuclear weapons programme or how the dismantling might be verified. Mr Trump said he wanted to see U.S. troops withdraw from the South. U.S. defence analysts have said Kim retains as many as 60 nuclear bombs and a range of missiles, including some he says can strike the US.
"Our understanding is that what President Trump said after his deep consultation with Chairman Kim Jong-un is aimed at strengthening the budding dialogue momentum between South and North Korea", said Kang, the South Korean foreign minister.
He tweeted: 'Just landed - a long trip, but everybody can now feel much safer than the day I took office. He tweeted Wednesday that "there is no longer a nuclear threat from North Korea" as a result of his work, and he has been critical of the press for its general disparagement of the summit.
In fact, it was previously reported by the Guardian that one of the vehicles in his convoy has a built-in toilet, which can only be used by him, and he even uses it within North Korea while conducting routine inspections at military bases and state-run factories!
"We believe that Kim Jong-un understands the urgency [of denuclearisation]", said Mr Pompeo.
"He (Trump) made it very clear that the condition precedent for the exercises not to proceed was for productive, good faith negotiations being ongoing", Pompeo told reporters.
After arriving in Seoul on Wednesday, Pompeo said he expected that North Korea would take major steps towards nuclear disarmament during Trump's first term.
Two North Korean missiles flew over Japan a year ago as North Korea made rapid advances in developing a missile capable of striking the USA mainland with a nuclear warhead.
To an extent Trump has pushed Moon Jae-in and Kim Jong-un into each other's arms, but that's not necessarily the best way to go about things.
Pompeo contradicted some claims from North Korean state media about what the process would look like.
Chinese state media described the summit as a "starting point" but said "no-one would expect the half-day summit to be able to iron out all differences and remove deep-seated mistrust between the two long-time foes".
After returning to the White House Wednesday, Trump also defended his decision to halt the joint military exercises with South Korea, which he called "war games" - a term used by Pyongyang - arguing on Twitter that the U.S. will "save a fortune". "But the issues of the alliance should be dealt with under the premise we maintain joint ironclad defence posture".
He said Kim affirmed an "unwavering commitment to complete denuclearization of the Korean Peninsula" in a signed document.
A spokeswoman for United States military forces in Korea said it had not received any direction to cease joint military drills.