It would've been hard to imagine the two leaders reaching this point just nine months ago.
Joseph Yun, former USA envoy for North Korea policy, alluded to that when he told a Senate hearing last week that there's a risk of "overloading the agenda" for the summit.
Trump said, "It's my honor - we will have a terrific relationship, no doubt".
Neither man smiled as they walked towards each other and grasped each others hand and then turned towards the cameras.
But Trump said, "We could absolutely sign an agreement and we're looking at it", adding, "Sounds a little bit unusual, but that's probably the easy part".
The two will huddle alone for roughly 45 minutes before being joined by aides for a larger meeting and working lunch.
He said he expected the Trump-Kim summit to "go fairly well" but added "people should not expect too much for the first time".
The White House did not immediately respond to questions about the call.
"I can only say this", Pompeo said. "If the talks fail, we could quickly go back to the kind of escalation we saw a year ago". The moves defused immediate threats of military action by the US.
A television screen shows news reader Ri Chun Hee announcing the arrival of North Korean leader Kim Jong Un to Singapore ahead of his meeting with US President Donald Trump, during an evening bulletin in Pyongyang on June 11, 2018.
The opening bid from the United States is the full and comprehensive dismantlement of North Korea's nuclear weapons infrastructure, from the warheads stored in the underground depots to the facilities that churn out the enriched uranium and the reprocessed plutonium.
North Korean leaders from past to present, from left to right: Kim Il Sung in 1980; Kim Jong Il in 2010; and Kim Jong Un in 2017; in Pyongyang, North Korea.
Pompeo said Monday the only acceptable outcome of the summit is "complete, verifiable and irreversible denuclearization" or dismantlement.
Trump has also said he would raise the issue of Japanese citizens abducted by North Korea, after Japanese Prime Minister Shinzo Abe lobbied him in a meeting in Washington last week.
Iizuka spoke highly of Trump's promise to include the abduction issue in the summit agenda along with the denuclearization of North Korea, hoping the return of the abductees will be ensured at the U.S.
The meeting, which will be held at the Capella Hotel, a secluded luxury resort on Singapore's Sentosa Island, will see the USA offering North Korea security assurances in return for complete denuclearisation, according to Secretary of State Mike Pompeo.
How likely is a breakthrough agreement?
Talks proceeded at multiple levels, including logistical discussions to allay Kim's fears of being deposed while traveling further afield than he ever has before as the country's leader.
Smart negotiations with Kim could help to rein in North Korea's nuclear activities and significantly disrupt Iran's efforts to improve upon its ballistic missile capabilities.
There is a chance for some history, however.
The talks will focus on North Korea's controversial nuclear programme.
For decades, North Korea has been a pariah state, and now its latest hereditary leader is being treated as a world statesman.
Following the meeting, Pompeo will travel to Beijing, Tokyo, and Seoul to brief regional powers on the talks. "We have our hostages, testing, research and all missle [sic] launches have stoped, and these pundits, who have called me wrong from the beginning, have nothing else they can say!"
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.