The US president says the two men are going to have a "terrific relationship" and that the summit will be "tremendously successful".
"Max Thunder" is an annual "war game" involving dozens of USA and South Korean fighters, bombers, and transport aircraft.
Pyongyang canceled pre-summit talks with Seoul last month, calling the "Max Thunder" military exercise "an intentional provocation running counter to the positive political development on the Korean Peninsula".
Trump and Kim met in Singapore on Tuesday and reached a short agreement that reaffirmed the North's commitment to "work toward complete denuclearization of the Korean Peninsula", but provided no details on when Pyongyang would give up nuclear arms or how that might be verified.
"U.S. troops are not bargaining chips to be offered up in an off-handed manner", Duckworth said in a statement. -South Korean exercises appeared off-limits under the new guidance.
But Victor Cha, a former U.S. pointman on North Korea, gave Trump more credit, writing in The New York Times: "Despite its many flaws, the Singapore summit represents the start of a diplomatic process that takes us away from the brink of war". The official acknowledged, however, it was still not certain how that was going to happen.
Pompeo said Trump would resume the military drills if North Korea stops negotiating in good faith. President Obama said that North Korea was our biggest and most unsafe problem. He also said the topic of pulling US troops out of South Korea did not come up in his meeting with Kim. No longer - sleep well tonight!'More news: Trudeau's criticism will cost Canada 'a lot of money'
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FILE PHOTO: The South Korean and American flags fly next to each other at Yongin, South Korea, August 23, 2016.
Critics, including in Congress, warn that an end to joint U.S. -South Korean drills could also erode the effectiveness of the military alliance between Washington and Seoul. Trump said: "That's true".
"The world will see a major change", he continued through a translator.
The August exercise, named Ulchi Freedom Guardian, has always been scheduled and final planning with several nations' military forces is well underway. "They're part and parcel of the same thing", said Lieu, who sits on the House of Representatives Foreign Affairs Committee.
Trump has been on a victory tour of sorts since he returned from the historic summit, where he was the first US president to meet with a sitting leader from North Korea.
Forces from Australia, Canada, Colombia, Denmark, New Zealand, the Netherlands and Britain also participated. "There is no longer a Nuclear Threat from North Korea", he tweeted in one of a series of early morning pronouncements. "At some point, I hope it would be", he said. That could give diplomats and military planners time. Trump has drawn bipartisan criticism at home for agreeing to pause joint U.S.
The declaration signed at the end of the summit said the two countries would co-operate towards "new relations", while the United States would provide "security guarantees" to North Korea.
One possibility could be carrying out some joint training overseas - beyond South Korea. Within the USA military's Pacific Command, there are plenty of regular exercise opportunities. "I'm not trying to unify South Korea and North Korea".