Those points were echoed in Monday's media coverage, which stressed that the talks with Trump would be focused on forging a relationship that is more in tune with what it called changing times - most likely meaning the North's new status as a nuclear weapons state - its desire for a mechanism to ensure a lasting a durable peace on the Korean Peninsula and, finally, denuclearization.
After the 2016 election, then-US President Barack Obama told Trump that North Korea was the biggest national security threat he faced, according to a US official.
Trump said one-on-one meeting with Kim Jong Un was "very, very good".
Iran's Foreign Ministry spokesman said Monday that it had "great pessimism" toward U.S. negotiations after Trump made a decision to back out of a U.S. -Iran deal - reached in 2015 under then-President Obama - that offered sanctions relief for Iran agreeing to curb its nuclear program.
European allies in North Atlantic Treaty Organisation - which Trump also blasted by tweet on Sunday - have criticized the President's decision to pull out of the Iran deal, and it is unclear how recent tensions may impact their support for whatever outcome the Singapore summit has.
Pompeo declined to comment on a question about the some 28,500 US servicemembers based in South Korea.
Mr Shanmugam is Singapore's Minister for Law and Home Affairs and he is responsible for ensuring security at the summit, the first between a sitting United States president and a North Korean top leader.
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Expectations are low that it will result in a major agreement on the North's nuclear weapons program, but the turn toward diplomacy has tamped down tensions that had raised fear of a nuclear war past year.
"I think within the first minute I'll know", he said.
Moon spokesman Kim Eui-kyeom also said Monday that Moon has no plans yet to speak with Trump after the meeting.
The meetings also served as an ice-breaker of sorts as the teams worked to get better acquainted after decades of minimal US-North Korean contact. Tuesday's meeting could pave the way toward a "new era of prosperity, security and peace", Trump said.
Trump has long groused about the cost of basing USA troops in South Korea and has floated the possibility of withdrawing them.
The summit will already be a significant PR coup for North Korea, which has sought a face-to-face meeting with the sitting USA president for decades.
Trump also reached Singapore on Sunday night.
Only hours before the White House announcement, US Secretary of State Mike Pompeo had seemed to lower expectations for the meeting, which Trump had earlier predicted could potentially yield an on-the-spot deal to end the Korean War.