The strategic insights of game theory experts like Thomas Schelling that shaped deterrence remain relevant as Trump constantly piled the pressure on Kim through a range of threats, from the ones he acted on like tough sanctions and others like strikes on North Korean facilities that he didn't.
The president also said it's possible Kim will make a trip to Washington in the future.
Added Trump: "So, I think the rhetoric, I hated to do it".
That deal reportedly includes a commitment to a "complete denuclearization" of the Korean peninsula aimed at establishing a "peace regime".More news: Kim summit highlights: European Union hails talks as 'crucial and necessary step'
One South Korean official said he initially thought Trump had mis-spoke.
The pledge, absent from the joint statement Trump signed with Kim, appeared to come as news to both South Korea and the Pentagon.
South Korean officials who met Kim this year said the North Korean leader said he understood the need for the training. "That's not part of the equation right now".
Only hours before the summit, Mattis told Pentagon reporters that, as far as he knew, the issue of United States troops in South Korea would not be part of any discussion in Singapore.
U.S. President Donald Trump's declaration on Tuesday that he meant to end joint military exercises in Korea seemed to be news to both South Korean and U.S. military officials.More news: Raptors promote assistant coach Nick Nurse to replace Casey
Only hours before the summit, Mattis told Pentagon reporters that, as far as he knew, the issue of U.S. troops in South Korea would not be part of any discussion in Singapore. "Was he committing to end all military exercises or was he committing to end just the most provocative ones?"
Pompeo added, President Trump is very prepared for his upcoming meeting with Kim Jong Un and is eager to achieve real progress.
Exercises with South Korea cover a range of eventualities, including drills with nuclear-capable bombers.
But Trump refused to endorse a communique at the G7 summit over the weekend that said participants were "guided by our shared values of freedom, democracy, the rule of law and respect for human rights and our commitment to promote a rules-based global order". "So I think it's probably well for everybody to maintain a healthy skepticism until we see those actions taken".
South Korean President Moon Jae-in spoke by phone with Trump for 20 minutes late on Tuesday, but an official readout of the call made no mention of military exercises.More news: Manchester United make a Positive Start in the Transfer Window
A favoured USA slogan in South Korea is "ready to fight tonight".