But the details of what is sure to be a complex and contentious process have yet to be settled.
"Right now, the USA and South Korea are not engaged [on troop withdrawal], and we're the only ones who make up our mind on this", he said. If the United States and North Korea - these completely opposite social systems who have never trusted each other - actually do end up with a solid agreement; if the president can shake hands with a really nasty dictator at the price of making peace; is anything out of reach?
"Just landed - a long trip, but everybody can now feel much safer than the day I took office".
Kim takes similar precautions during his travels inside North Korea to inspect military bases and state-run factories, according to South Korea news agency DailyNK.
Speaking in South Korea, where he discussed the outcome of the summit, Secretary Pompeo said there was still "a great deal of work to do" with North Korea.
Pompeo also said he was very confident that "sometime in the next week or so we will begin the engagement" with North Korea, though he didn't know the timing or how meetings would be structured. Still, others might say let's wait until there's an actual peace deal before we start doling out the accolades. "Propaganda, all that stuff, that's not something we'd get involved in".More news: How can Roger Federer return to world number one?
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Canada's small community of North Korean defectors has been shocked and infuriated by Trump's contrasting treatment of the two leaders: insults for Justin Trudeau after the G7 meeting in Quebec and flattery for Kim Jong-un at the summit in Singapore. He said negotiations would recommence "in the next week or so".
U Sung Tak, 79, said the future was looking "bright" because Kim was "leading the world's political trend on the Korean peninsula, steering the wheel of history". While the president won general praise for talking to Kim - instead of tweeting at him - even some Republicans were grasping for concrete takeaways and sounding cautious. The Bill Clinton and George W. Bush administrations both did so.
But the brief document from the two leaders' historic meeting provided no details on when Pyongyang would give up a nuclear weapons program that has advanced enough to threaten the United States, or how the dismantling might be verified. But if Trump seeks re-election in 2020, his government is likely to apply more pressure on North Korea to make substantial progress in denuclearization, which could bring the nuclear issue to another critical point, said Shin Beomchul of Seoul's Asan Institute for Policy Studies. A year ago it tested long-range missiles that could reach the USA mainland, although it remains unclear if it has mastered the technology to deliver a nuclear warhead that could re-enter the atmosphere and hit its target.
The move - long demanded by Pyongyang - has been seen as a major concession to North Korea and appeared to take U.S. allies in the region by surprise. President (Barack) Obama said that North Korea was our biggest and most unsafe problem. "No longer - sleep well tonight!"
The unprecedented, one-on-one meeting in Singapore Tuesday aimed to kickstart a process that would lead to denuclearization on the Korean peninsula and resolve seven decades of hostilities between the world's largest nuclear power and the isolated pariah state.
The KCNA report - which was also carried by the Rodong Sinmun, official newspaper of the ruling Workers' Party - also claimed that the president pledged to suspend military drills with South Korea, and lift sanctions on the North. Trump's announcement appeared to catch the Pentagon and officials in Seoul off guard, and some South Koreans were alarmed.
Trump also is wrong in saying "nothing happened" in return.
At his news conference, President Trump said it was hard to ensure anything but that he trusted his instinct that Mr Kim would abide by his word.