For Trump, cutting a deal to end the North Korean nuclear threat with his approach to Kim, in defiance of the US security establishment's long-held ways of dealing with the North, would be a success unmatched by any predecessors.
At 10am, North Korean vice-minister for foreign affairs, Choi Sun-hee, strode into the Ritz Carlton with her small team.
The sudden change in schedule added to a dizzying few days of foreign policy activity for Trump, who shocked USA allies over the weekend when he used a meeting of the Group of Seven industrialized economies in Canada to alienate America's closest friends in the West. Lashing out over trade practices, Trump lobbed insults at his G-7 host, Canadian Prime Minister Justin Trudeau. "I think that very quickly I'll know whether or not something good is going to happen", Trump predicted Saturday.
KCNA's coverage also highlighted Mr Kim's late-night stroll in Singapore, and said the leader was impressed by a "nocturnal bird's eye view" from the top of the Marina Bay Sands hotel, where a SkyPark links three 55-storey towers.
Hours earlier, a jet carrying Kim landed.
"It's hospitality that we would have offered them, and as Chairman Kim said yesterday, he would have liked to have come to Singapore anyway, with or without the summit", Singapore Foreign Minister Vivian Balakrishnan told the BBC.
Kim smiled broadly Sunday evening as he met with Singapore Prime Minister Lee Hsien Loong.
Trump is set to meet with Lee on Monday.
Rodman appeared in Trump's Celebrity Apprentice reality TV show, only to be booted off because he misspelled Melania Trump's name.
In part, these lowered expectations are a reflection of the extreme skepticism among many that the North can be persuaded to give up a nuclear programme it has stubbornly built over the decades, often in secrecy and despite intense sanctions, global condemnation and widespread suffering among its people. We will keep building our buildings and our missiles.
The top U.S. and North Korean negotiators held a last-ditch meeting in Singapore on Monday to try to narrow the gap between the two sides on what denuclearisation by North Korea should look like.
It is the first time sitting leaders from both countries have ever met and marks a remarkable turnaround in the men's personal relationship.
Despite the optimism, it's unclear whether the gap between the United States and North Korea over what denuclearization means has been bridged.
Trump is hoping to get Kim to agree to get rid of his nuclear weapons, though he has said it may take many more meetings to get to that point.
The summit has officially begun, with Trump and Kim shaking hands and posing for photographs. The war was concluded with a truce, not a peace treaty, but a treaty will also have to include China, which was party to the armistice. Meanwhile, Mr Kim has called Mr Trump "mentally deranged" and a "dotard".
Participants in a mass rally gather in Kim Il-Sung Square in Pyongyang on September 23, 2017.
He said about half of the cost is for security. Pyongyang's weapons program benefits from forced labor.
Any nuclear deal will hinge on North Korea's willingness to allow unfettered outside inspections of the country's warheads and nuclear fuel, much of which is likely kept in a vast complex of underground facilities. In 2013, the 57-year-old visited North Korea to host basketball exhibitions with the Harlem Globetrotters as part of a VICE documentary.