Only a few months ago, Kim and Trump were swapping personal insults such as "dotard" and "little rocket man" and the North conducted its sixth and most powerful nuclear test, as well as firing missiles over Japan.
There have been inconsistencies in remarks from other top USA officials on whether sanctions will only come after complete denuclearization, or may be eased along the way.
Although human rights was not included in the joint statement signed by Trump and Kim, the U.S. president said he raised the issue and he believed the North Korean leader wanted to "do the right thing".
"We will be stopping the war games, which will save us a tremendous amount of money, unless and until we see the future negotiation is not going along like it should", Trump said in Singapore.
North Korea is believed to possess more than 50 nuclear warheads, with its atomic program spread across more than 100 sites constructed over decades to evade global inspections. "No longer - sleep well tonight!"
Without any prior warning, Trumpannounced he will be suspending the annual U.S.
Most Western observers have said the deal includes no new commitments from North Korea nor details on how denuclearisation could be achieved or verified. "That will take a while".
Shares in Butan Industrial dipped further off their recent highs following Trump's get-together with Kim Jong Un, closing around 10% lower.
The North's official KCNA news agency described the summit as an "epoch-making meeting" that would help foster "a radical switchover in the most hostile [North Korea]-US relations".
"We will be stopping the war games which will save us a tremendous amount of money", Trumptold reporters, adding that "at some point" he wanted to withdraw USA troops from the South.
"The United States is our ally, so the joint military drills are still necessary to maintain our relationship with the USA", said Lee Jae Sung, from Incheon. I don't think they are recording it.
Secretary of State Mike Pompeo arrived at Osan Air Base south of Seoul from Singapore early Wednesday evening.
Pompeo was scheduled to travel next to Beijing before returning to Washington. It has arguably gotten more brutal under the 34-year-old third current dictator, to whom Mr. Trump was so courteous and even complimentary in their Singapore meetings.
But Panetta, who previously worked for President Barack Obama, said there are a "huge number of issues" that will actually involve the denuclearization of North Korea, which owns an estimated 20 to 60 nuclear weapons with about 141 sites that can produce them.
"We save a fortune by not doing war games", Trump tweeted Wednesday, "as long as we are negotiating in good faith - which both sides are!"
Critics at home said the joint statement by the two leaders was short on detail and that Trump had made too many concessions to Kim.
The White House did not immediately respond to the North Korean characterisation of the deal. The next military exercise is scheduled for August. It said that he had also agreed to "step by step" denuclearization, rather than the rapid and irreversible process the administration said it was demanding.
In China, Chinese Foreign Minister Wang Yi told reporters that the fact that the two leaders "can sit together and have equal talks has important and positive meaning, and is creating a new history".
About 29,000 United States soldiers are based in the South, under a security agreement reached after the war ended in 1953. -South Korean drills was met with concern.
The Pentagon has denied that US Defence Secretary Jim Mattis was caught off guard by the president's announcement, saying "there were no surprises". He said he planned to continue sharing the view with Washington and Seoul.
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