"Just landed - a long trip, but everybody can now feel much safer than the day I took office", he tweeted.
Of the world's eight known nuclear powers beyond North Korea, three - India, Pakistan and Israel - emerged outside a formal global arms control framework.
He lauded the joint statement of bare-bones principles as a comprehensive denuclearisation agreement, when to many seasoned observers it didn't constitute anything close to a disarmament agenda binding Kim Jong-un to action. North Korea is a real and present threat.
"Trump has pulled off something that could make him a man of history and strengthen his America First project - howsoever unpalatable the thought is that Trump might become a victor in the overall bargain", said MK Bhadrakumar, a former diplomat and commentator. He said negotiations would recommence "in the next week or so".
On Tuesday, Trump and Kim signed a statement outlining four points, including reaffirming a commitment to denuclearize the Korean peninsula. "He was not leaving the summit without claiming he made a deal", Kimmel said.
The presentation bemused those of us packed into the press hall - we thought at first it was North Korean propaganda. "They are fighting hard to downplay the deal with North Korea". -South Korea military exercises could be put back on if talks with Pyongyang do not progress. Pompeo, the former Central Intelligence Agency director, then plans to fly to Beijing to update the Chinese government on the talks.
Trump on President Xi of China: "He's an incredible guy".
There has been deep scepticism about the agreement, with observers saying it lacked detail on how North Korea would give up its nuclear weapons and how that process would be verified. Saddam gave up his nuclear program and died; Qaddafi gave up his program and died; Kim didn't give up, built a bunch of nuclear weapons and not only stays alive but gets rewarded. Past year 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. "Yeah, but so have a lot of other people have done some really bad things", Trump said, adding, "I mean, I could go through a lot of nations where a lot of bad things were done".
Through a translator, North Korea's leader summed up the surreal nature of the meeting, telling the U.S. president that those watching around the world might see it as "a science fiction movie".
But he said that was no longer the case, and everyone can "sleep well tonight". Mr Trump made clear he was keeping USA sanctions in place until he saw evidence of a reduced nuclear threat.
Trump has been criticized for already announcing the halting of "war games", or military exercises, with South Korea, a move long sought by Pyongyang.
While Mr Trump has confirmed Mr Kim has agreed to work toward complete denuclearisation of the Korean Peninsula, it was only briefly referenced twice in the article. Trump cast the decision as a cost-saving measure, but also called the exercises "inappropriate" while talks continue. "I got them after we had signed the agreement".
"He was unambiguous about that", Pompeo said.
US critics of the deal said it was short on details and that Trump had made too many concessions to Kim, especially the USA leader's unexpected announcement that the United States is ending its military exercises with South Korea, long an irritant to North Korea.
The traditional USA calendar for other major drills would not pick up again until next spring, officials say.