In a joint statement issued after their historic summit, Mr Trump and Mr Kim said they agreed to improve their countries' relationship, a move that would inevitably require a formal end to the Korean War, in which almost half a million American troops fought with their South Korean allies.
Republican Sen. Lindsey Graham of SC, however, takes the opposite point of view.
Moon Seong Mook, a former South Korean military official, said Trump's comments on the drills confirmed what many in South Korea had feared all along - that North Korea would attempt to drive a wedge between Washington and Seoul and gain substantial concessions from an unconventional USA president who thinks much less of the traditional alliance than his predecessors.
However, dismantling Pyongyang's nuclear weapons programme will present a daunting challenge.
"We will stop the war games which will save us a tremendous amount of money", the USA president said at the press conference after the talks. The North has traditionally railed against the joint exercises and charged that they are practice for an invasion. And Donald Trump is not going to capitulate.
While most of the agreements confirmed to have come out of the Trump-Kim summit were pretty straightforward, advancing on the already discussed denuclearization, the meeting also ended with an announcement that the U.S. will suspend all joint military exercises with South Korea.
When Stephanopoulos asked Graham about this anomalously hawkish letter from his Democratic colleagues, Graham challenged them: They must vote to authorize war.
"Kim should be the most likely partner of Pompeo, having worked with him before and knowing well about what Kim Jong Un wants", said Cheong Seong-chang, a North Korea leadership expert at the Sejong Institute south of Seoul.More news: Reminding Russia About Its Lost Seat at the G7 Table
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On Wednesday Trump framed this as a win, saying the United States will now "save a fortune".
What would a new Korean War look like? "We'll see what happens tomorrow".
"It would be very, very serious war", he said.
Foster Klug is AP's bureau chief in South Korea and has covered the Koreas since 2005.
Moon tried to put the issue to rest, saying, "The USFK is a matter of the Seoul-Washington alliance", but now seems to find himself at sea. If this goes a little longer the whole country will collapse, and the President Trump, I hope he doesn't pour the money into save that man. "We will be successful in accomplishing our objectives", Dunford continued.
"I'm equally confident in what Secretary Mattis said", he added. There are also joint US-Japanese drills each year.
"We understand what the United States and its allies mean".