The source said halting the joint exercises was one of "many tools in the tool box" that the President took with him to meet with Kim but the final decision on what concession or concessions he would make wasn't determined until he was able to size up Kim.
"I'm not for Russian Federation, I'm for the United States", Trump said.
Trump on Tuesday seemed fine with this, saying he thought Kim was being honest.
"What's really disconcerting is that Trump announced unilaterally to the leader of North Korea that the United States is going to stop military exercises with our allies, without first telling our allies or even the Pentagon", Michael Green, a senior vice president for Asia at the Center for Strategic and International Studies, told Yahoo News on Tuesday.
But the USA president trumpeted the outcome as a "deal" with North Korea and vowed there would be "no more rocket launches, nuclear testing or research!"
With both annual "war games" concluded until 2019, Trump now has time to hammer out a concrete agreement on denuclearization with Kim, details of which were scant in the deal signed between the two leaders. He said that the concepts were encompassed within the word "complete".
Despite the uncertainties, Trump talked up the outcome of what was the first meeting between a US and North Korean leader in six decades of hostility.
The Facts: He's wrong in suggesting his administration is the first to start on denuclearization with North Korea.
"One can't completely denuclearize without validating, authenticating". "The country has an extensive network of sites and underground tunnels that can be used to hide material".
KCNA quoted Kim as saying that the North can take unspecified "additional good-will measures of next stage commensurate with them" if the U.S. takes genuine measures to build trust.
"There is no limit to what NoKo can achieve when it gives up its nuclear weapons and embraces commerce & engagement w/ the world".
"Oh we know that's what you do", Stephen Colbert shot back in a comment on The Late Show.
In return, Mr Trump, to the surprise of US ally South Korea and his own military, said he would end joint US-South Korea military exercises. Trump promised to provide security guarantees to the North and suspend joint military drills with the South as long as negotiations with the North continue in "good faith".
Sen. Lindsey Graham does not have an issue with halting joint military exercises between the US and South Korea while discussions with North Korea continue. The term "war games" was also a term coined by China and North Korea.
The likelihood of Kim Jong Un launching a first strike against the US, thereby bringing on "fire and fury", was low. North Korea is a real and present threat. But the White House "tried to fill in the blanks", he said, and in Kimmel Live's imagining, Trump gave away a comically large number of things. "I hate to appear a businessman, but I kept saying, what's it costing?"