After arriving back in the USA, the president also tweeted that "everybody can now feel much safer".
Trump, who returned to Washington early on Wednesday, hailed the meeting with Kim, the first between a sitting U.S. president and a North Korean leader, as a success that had removed the North Korean threat.
After almost five hours of unprecedented talks between Trump and Kim on Tuesday, the two leaders signed a document in which Kim "reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula" and the United States agreed to "provide security guarantees".
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".
Yet he immediately faced pointed questions at home about whether he got little and gave away much in his push to make a deal with the young autocrat - including an agreement to halt United States military exercises with South Korea. "No longer - sleep well tonight!"
Almost an hour later, noted the "fortune" the USA will save as a result of his commitment to end U.S.
The US and its ally South Korea hold regular military exercises to the fury of North Korea, which has long seen the drills as preparations to invade it.
For weeks, Pompeo and other officials have insisted North Korea must agree to "complete, verifiable, irreversible denuclearization" before economic sanctions can be lifted. There is no longer a Nuclear Threat from North Korea.
It says the sides "commit to establish new US-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity". "We overcame all kinds of scepticism and speculations about this summit and I believe that this is good for the peace", he said.
In the U.S., supporters of President Trump welcomed the outcomes of the summit as a historic breakthrough.
In just one example of the uncertainty after the meeting, it emerged that Trump had offered Kim "security guarantees" - a phrase that usually connotes military protection, which can not possibly be what Trump meant.
"The U.S. -South Korea joint exercises and U.S. forces in South Korea play significant roles for the security in East Asia", Japanese Defence Minister Itsunori Onodera told reporters Wednesday.
In comments reported by Reuters, he said there was still "a great deal of work to do. a long way to go with North Korea". -South Korean drills was met with concern.
Trump and Kim wrote of a new future for the world in their joint statement, but that new future may be one ruled from Beijing, not Washington. A flurry of media coverage the day Kim arrived in Singapore showed him waving from the door of the specially chartered Air China flight that brought him from Pyongyang. "However we think that it is crucial to pursue various solutions for better dialogue".
Joint military exercises between US and South Korean troops have long angered Pyongyang. He said he planned to continue sharing the view with Washington and Seoul.
Trump also offered North Korea security guarantees. It will be the first ever meeting between a sitting US President and North Korean leader.