At the end of the historic summit, Trump and Kim signed a joint statement to put in writing the commitment to a denuclearized and peaceful Korean Peninsula. It was shocking, he said, because these exercises are fundamental to our military relationship with South Korea.
"South Korea will have mixed feelings toward Trump's remarks", said Lee Il-woo, a director at Korea Defense Network in Seoul.
"I hope - but am not yet confident - that (North Korea) will take steps that match the concessions Mr. Trump has already made by ending military exercises in South Korea and granting Mr. Kim legitimacy with this summit", Thomas Countryman, a former acting under secretary of state for arms control under President Barack Obama, told Reuters. The South Korean military seemed similarly surprised.
USA forces in South Korea said it has "received no updated guidance on the execution or cessation of training exercises" and will continue to coordinate with South Korean partners and maintain the current posture until it receives an updated guidance from the Department of Defense or the Indo-Pacific Command. "And these training exercises - the president calls them "war games" - are for the defense of South Korea".
He added that it's "totally premature" to discuss the United States withdrawing its nuclear umbrella from the Korea peninsula in exchange for the total denuclearization of North Korea. "Plus, I think it's very provocative".
One South Korean official said he initially thought Trump had mis-spoke.
Analysts generally agree that a series of stringent economic and financial sanctions against North Korea, led by the U.S. with China's support, have played a big role in Kim's sudden embrace of diplomacy in the past six months after his repeated nuclear provocations.
North Korea's state media, referring to the drills, recently demanded that Washington "stop the acts of threatening its dialogue partner by force".
Trump on Tuesday announced joint U.S.
"So I think the rhetoric, I hated to do it, sometimes I felt foolish doing it, but we had no choice", he said.
A spokeswoman for US military forces in Korea, meanwhile, said it had not received any direction to cease joint military drills.
Purdue, who has lived in Singapore and China as a businessman before his political career, said it would "be bad to throw on there any concession except for economic development" in negotiating the denuclearization of North Korea.