"Everybody can now feel much safer than the day I took office", Trump said on Twitter.
Trump, who returned to Washington early on Wednesday, hailed the meeting with Kim, the first between a sitting USA president and a North Korean leader, as a success that had removed the North Korean nuclear threat.
Kim said "to achieve peace and stability of the Korean Peninsula and realize its denuclearization", North Korea and the United States "should commit themselves to refraining from antagonizing with each other", according to North Korean media.
Despite Trump's optimism following his summit with Kim, many remained skeptical that North Korea, infamous on the world stage for making empty promises, especially when it comes to its nuclear program, would follow through on its pledges from this week's meetings.
In another political win for President Xi Jinping, the declaration was effectively a tacit acceptance of the "freeze for freeze" proposal pushed by Beijing a halt to both US-South Korea joint drills and the North's weapons tests.
Almost an hour later, noted the "fortune" the US will save as a result of his commitment to end U.S.
Mr Trump also unexpectedly announced United States would not hold war games with South Korea while North Korea negotiated in good faith on denuclearisation.
Best case scenario is the two sides start talking, North Korea decides the U.S.is no longer a threat and scales back its arsenal.
The Korean Central News Agency (KCNA) reported that Kim and Trump agreed 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". The document signed by the leaders at their historic summit Tuesday also says they will join efforts "to build a lasting and stable peace regime" on the Korean Peninsula.
Trump, seemingly unprompted, has long wanted to withdraw the US from South Korea, and now he may have found a reason.
Trump acknowledged that his agreement with Kim Jong Un is not foolproof. Incidentally, Trump's announcement apparently surprised South Korean President Moon Jae-in's government in Seoul. "The V matters", he told reporters. Trump has drawn bipartisan criticism at home for agreeing to pause joint U.S.
Echoing North Korean language, Mr Trump described the military exercises as "very provocative". "All that I think gave them confidence that this was the right site, the right choice".
Pompeo, speaking to reporters in Seoul on Wednesday, sought to quell criticism that North Korea didn't make any major commitments at the summit in Singapore.
A suite on the 20th floor of St. Regis Hotel, where Kim is staying, costs more than 13,000 Singaporean dollars a night. He said he planned to continue sharing the view with Washington and Seoul.
There are usually two sets of exercises every year, in spring and autumn, involving a massive number of troops and military hardware.
Any reduction in tensions on its doorstep is welcome for China, North Korea's closest ally, which accounts for around 90 percent of Pyongyang's trade.
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