However, Leong said both found it hard to hide their nervousness once they were seated, with Trump displaying a slanted smile, and fidgeting with his hands and Kim leaning and staring at the ground.
While President Trump has spoken positively about the upcoming summit, he has been vague on details of what they might be able to actually achieve.
Yet Trump and Kim have yet to agree even on how to define denuclearization of the Korean peninsula - the stated goal of the meeting.
"Yes, Donald Trump reached out", Rodman said, telling Cuomo he'd received a call from a person he described as Trump's secretary. Korean Central News Agency (KCNA) mentioned that the summit is being held "under the great attention and expectation of the whole world".
"The complete and verifiable and irreversible denuclearization of the Korean Peninsula is the only outcome that the United States will accept", US Secretary of State Mike Pompeo told reporters before the summit began.
As the two leaders met, Singapore navy vessels, and air force Apache helicopters patrolled, while fighter jets and an Gulfstream 550 early warning aircraft circled. "But we overcame all of them, and we are here today", Kim said during the meeting through an interpreter.
"I think that I brought awareness to a lot of things around the world and I think North Korea has given a lot of people the opportunity to do this conference now and I hope it's a success".
EU’s Michel Barnier instantly rejects Theresa May’s Brexit backstop plan
The Daily Mail last month ran a front-page headline on Best for Britain's plan reading: "Plot to subvert Brexit exposed". The May proposals also failed to address the need for full regulatory alignment on either side of the border, he added.
Flight from Pyongyang lands in Singapore ahead of North Korean leader’s arrival
North Korean leader Kim Jong Un has only said he's willing to discuss the idea, but hasn't made any firm promises to do so. Skeptics also warn about the dangers of ridiculously high expectations surrounding the summit.
DPRK leader Kim Jong Un arrives in Singapore for summit: foreign ministry
Media captionTrump-Kim summit: Can you achieve peace on a plate? Kim smiled broadly yesterday evening as he met Lee. US President Donald Trump has arrived in Singapore for Tuesday's historic summit with North Korea's Kim Jong-un.
President Donald Trump and North Korean leader Kim Jong Un shared a historic handshake as they met for the first time.
The president is now in Singapore, just hours away from his historic meeting with Kim. North Korea's supreme leader seeks a formal end to that war, which has frozen the Korean peninsula in a state of conflict throughout the modern era and has kept almost 29,000 USA troops indefinitely stationed in the south, as well as an injection of foreign direct investment. Mr Kim, speaking via a translator, said: "It wasn't easy to come to this point".
It is the first time a sitting USA president has ever met a North Korean leader. I got so many death threats.
It was the first time a sitting U.S. president met a North Korean leader.
Sitting across Mr Kim and his team at the larger meeting was the USA leader, his chief of staff John Kelly, secretary of state Mike Pompeo and national security adviser John Bolton.
He said if diplomacy fails to move in the right direction, the sanctions "will increase".
Former US basketball star Dennis Rodman wept during an interview in Singapore on Tuesday as he discussed unprecedented talks between the North Korean and US leaders in the city-state aimed at trying to end a nuclear standoff.