The two leaders are staying in separate hotels, not far from each other.
President Trump has said the best-case scenario is not going to resolve all these issues.
He continued: "But in the end, that doesn't matter".
Rodman, who was once a contestant on Trump's reality TV show "The Apprentice", said he once gave Kim a copy of Trump's book "The Art of the Deal" to help him understand the USA president better.
President Moon played an important role in breaking the ice between Trump and Kim and played his role in paving a way for this historic summit.
North Korea, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Kim's dynastic rule. Choe is the Vice Foreign Minister for the North Korean Foreign Ministry.
Kim was cheered by onlookers who caught sight of the dictator, who until earlier this spring was not believed to have ever left North Korea as supreme leader.
New details of the agenda have been released. At the same time, he'd admitted he didn't believe he required extensive preparation to take stock of Kim.
What are the talks about?By contrast, Trump appeared to back off a military footing on Tuesday, declaring the United States will stop the "war games", an apparent reference to joint military exercises with South Korea that North Korea has long rebuked as provocative.
"They have to de-nuke".
Although gaps remain over what denuclearisation would entail, Trump sounded a positive note in a lunch meeting with Singapore's Prime Minister Lee. Missile tests, nuclear tests, and sinking a South Korean warship followed, causing the United Nations to impose even tougher sanctions. The 1950-53 conflict ended with a truce, not a final peace treaty.More news: Three Californias? Measure to split state heads to November ballot
But some question why Kim should trust any guarantees given Trump's history of pulling out of accords - most recently the painstakingly negotiated Iran nuclear deal.
The Trump administration will only accept complete denuclearisation of the North, Mr Pompeo stressed.
Close US ally Japan has urged Trump to bring up the decades-old issue of its citizens abducted in 1970s and 1980s to train Pyongyang's spies in Japanese language and customs.
He expressed hope that Trump and Kim would be able to make progress.
North Korea has repeatedly expressed a commitment to the "denuclearisation of the Korean peninsula" - notably in a report by state agency KCNA on the eve of the summit - but the term is open to interpretation on both sides and it remains unclear what concessions Kim is prepared to offer.
Kim says through an interpreter that it "was not easy to get here" and that there "were obstacles but we overcame them to be here".
Word of the private tete-a-tete unleashes a torrent of criticism from national security veterans who say having aides present in high-stakes meetings provides protection and ensures no one can misrepresent what transpired.
Talks of this kind typically take months to prepare.
The White House said later that discussions with North Korea had moved "more quickly than expected" and Trump would leave Singapore on Tuesday night after the summit, rather than Wednesday, as scheduled earlier.