Some pro-military South Koreans feel deeply betrayed by President Trump's surprise announcement about suspending joint armed forces drills, which have been the most vivid display of the U.S.
"We would like to seek an understanding of this between Japan, the USA and South Korea", Japan's defence minister, Itsunori Onodera, said. He also said he'd like to remove all 28,500 USA troops stationed in the South, although he made clear this was an option for the future, not a part of current negotiations.
The U.S. has stationed combat troops in South Korea since the end of the 1950-53 war and has used them in a variety of large-scale drills created to sharpen skills and test troops' ability to operate effectively with their South Korean partners.
"There's three outcomes here: Peace, where we have a win-win solution", Graham said.
While many support the close military co-operation with the U.S. as a key ally for the security it provides, critics say they are an unnecessary provocation and stand in the way of easing tensions with Pyongyang.
"The absence of the North Korean name in the joint statement, despite the role that Kim Yong Chol has played so far, could mean Kim Jong Un is agonising over whether he should now charge diplomats to do the job", said Shin Beom-chul, a senior fellow at the Asan Institute for Policy Studies in Seoul.
Trump described his meeting with Kim as "better than anyone could have expected".
"It feels like there is a big change coming with this", she said.
At the same time, he noted that the U.S. forces' deployment in South Korea had not been discussed with Kin Jong Un.
Also, the USA forces stationed at South Korea admitted that Department of Defense or the Indo-Pacific Command had given them "no updated guidance on the execution or cessation of training exercises" and hence will continue to coordinate with their Seoul counterparts and maintain their current positions until further notice.
Seoul accused him of masterminding deadly attacks on a South Korean navy ship and an island in 2010.
That was apparently the message delivered by Vice President Mike Pence to Senate Republicans during a private lunch earlier Tuesday, according to Sen. Cory Gardner, R-Colo. - although that was immediately disputed by Pence's office.
Declining tensions with North Korea and the lack of major war games is also likely to spark discussions about cutting United States troop levels in South Korea.
As of Tuesday morning, U.S. Forces in Korea are still moving ahead with plans for the annual exercise known as Ulchi Freedom Guardian.
According to the Pentagon, about 28,500 US troops are stationed in South Korea. In his view, preparedness equates to more effective deterrence - persuading potential adversaries they can not win and thus should not attack.
Away from the TV, the former "Rocket Man", now respectfully recast in Trump terminology as "Chairman Kim", did strike a formidable coup by completely erasing the dreaded acronym CVID - or "complete, verifiable, irreversible denuclearization" - from the final text of the Singapore joint statement.
'The test now is this declaration that was signed with the US President in front of the world's media that must stand, and the onus now is on North Korea to prove that it's genuine, ' she told reporters.
Even some Republicans in Congress seemed uneasy about this.
With that said, in recent days the White House has emphasized Tuesday's meeting will be the first step in a broader process. This led to North Korean condemnation, and Trump briefly cancelling the summit.
The reporter then corrected himself, saying "South Korea" before Mr Turnbull said "ah right, OK" and proceeded to answer the question.
On the other hand, Russian Federation and China, who joined North Korea in criticizing the joint military drills in the past, welcomed Trump's decision.
He also believes this deal will hurt America and South Korea financially.
Klug reported from Singapore.
Foster Klug is AP's bureau chief in South Korea and has covered the Koreas since 2005.