South Korean ambassador Baeksoon Lee also said Mr Trump's "bold, top-down leadership" had made this week's landmark Singapore summit possible, heralding a "new chapter of history" that will need to be backed up with concrete and verifiable steps towards North Korean denuclearisation.
There were worries, especially in Tokyo and Seoul, which have huge US military presences, about Trump agreeing to halt USA military exercises with South Korea, which the North has long claimed were invasion preparations.
Trump, seemingly unprompted, has long wanted to withdraw the US from South Korea, and now he may have found a reason.
Will Trump demand the same standard in his negotiations with the North Koreans, insisting that Pyongyang offer inspectors historically invasive access to its military facilities?
Joel Wit, a Stimson Center senior fellow and North Korea expert, told NPR that in such a timeline "you could probably disarm key portions of the North Korea nuclear program". He then told the reporter he found the question "insulting and ridiculous and, frankly, ludicrous". "Let me assure you that the "complete" encompasses verifiable in the minds of everyone concerned". He said that the concepts were encompassed within the word "complete". "And, I'll be honest, we are being taken advantage of by virtually very one of those countries".
Thirty-nine percent believe the summit has lowered the threat of nuclear war between the United States and nuclear-armed North Korea, slightly more than the 37 percent who said they did not believe it changed anything.
Moon has championed engagement with the North, and the agreement's language on North Korea's nuclear program was similar to what the leaders of North and South Korea came up with at their own summit in April. He told reporters that if the USA concludes they no longer are, the freeze "will no longer be in effect".
"I think he will start that process right away", Mr Trump said.
Tokyo has expressed some concern about the cancellation of military exercises.
Late a year ago, for example, she announced North Korea's test of what it said was a hydrogen bomb, telling viewers it was a "perfect success".
"Apparently, Washington and Pyongyang are moving exactly in this direction", Russian Foreign Minister Sergei Lavrov told reporters in Moscow.
Apple is going to ruin cops’ favorite tool for breaking into iPhones
The FBI claims it has at least hundreds of electronics devices connected to investigations that it can't access due to encryption. But in 2016 Apple refused to help police unlock a phone used by a gunman who killed 14 people in San Bernardino, California .
Trump has been criticized for lending legitimacy to the North Korean dictator, whose regime has an atrocious human rights record, by attending the meeting in Singapore.
Pompeo sought to counter concerns that North Korea and the U.S. came away from the talks with fundamentally different interpretations.
But no rational and objective observer who followed the summit and saw Trump and Kim behaving so cordially can believe that Trump is leading the USA into a nuclear war with North Korea.
During the summit in Singapore on Tuesday, Kim said there are possibilities for him to meet with Abe, according to the source.
"Kim Jong Un and Trump had the shared recognition to the effect 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", state media outlet KCNA reported.
"President Trump appreciated that an atmosphere of peace and stability was created on the Korean Peninsula and in the region, although distressed with the extreme danger of armed clash only a few months ago, thanks to the proactive peace-loving measures taken by the respected Supreme Leader from the outset of this year", the North's state-run Korean Central News Agency said in a summary of the meeting.
That discussion between Putin and Trump reportedly happened in summer 2017.
The sanctions regime that has placed unprecedented restrictions on the North Korean economy is now likely to slip.
"Trump has pursued what he calls a "maximum pressure" campaign" against Pyongyang to force it to give up its nuclear weapons.
Pompeo said the brief, four-point joint statement that emerged from the summit did not encapsulate all the progress the USA and North Korea had made.