The summit between the two leaders occurred on Monday evening United States time and Tuesday in Singapore, ending with Trump and Kim vowing to "denuke" North Korea. According to current reports, it ended amicably with the two shaking hands and smiling, though details of their plan still need to be hashed out.
Israeli ministers, meanwhile, have welcomed the Trump-Kim summit for the message it sends to Iran.
Trump and Kim's joint pledge to work toward "complete denuclearisation of the Korean peninsula" was widely interpreted as failing to convince North Korea to accept Washington's definition that calls for Pyongyang to get rid of its arsenal.
"The greatest achievement of the summit was that Trump's comments show his confidence in resolving any issues [with Kim]", Nam said in a brief meeting with a small group of reporters in Singapore.
In response to Trump's suggestion that an agreement to formally end the Korean War might take place soon, Nam said the Moon administration would not hasten the process and that there was "no timeframe" set for the process.
Despite extensive denuclearisation since the Cold War, FAS estimates 1,800 US, Russian, British and French warheads are on high alert, ready to be used at short notice.
"Now would not be the time to ease worldwide sanctions against North Korea".
American adults have supported working toward denuclearization of North Korea using diplomacy and peaceful efforts for many years. "The fact that I am having a meeting is a major loss for the U.S., say the haters & losers", he tweeted.
Trump had agreed to halt joint military exercises with South Korea after the North Korea summit.
But analysts warned there were still big challenges ahead, especially since the two sides failed to reach any specific agreement on dismantling North Korea's nuclear weapons - a threat on China's doorstep.
US 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.
Trump insisted at a post-summit news conference that this was the start of a process and that sanctions would remain in place until Kim takes concrete steps toward denuclearisation. -South Korea military exercises, which he and North Korea both called provocative.