But today, a top South Korean official warned that "significant" differences remain between the two sides on how to achieve denuclearisation.
The two teams in Singapore are tasked with working out the logistics of the summit, including venue spaces, transportation, security and group photographs. They face a daunting target date of June 12, and the knowledge that a failed meeting could increase the chances for military confrontation between Washington and Pyongyang.
"We must remember that modern-day summits between two nations are completely scripted affairs - no detail, agenda item or deliverable is left to chance," said Harry Kazianis, an Asia expert at the Centre for the National Interest. "These take months to negotiate, and considering the stakes for North Korea and the United States, the outcome must be determined before the meeting."
Kim has expressed an unusual degree of interest in the summit's logistics, asking Secretary of State Mike Pompeo during his visit to Pyongyang this month about fuel for the 9655km round-trip flight to Singapore and how many body guards he could bring, according to people familiar with the conversations.
Although most logistics teams would be led by a low-level bureaucrat, Kim sent his de facto chief of staff Kim Chang Son, one of the country's most powerful officials, to head the North Korean team. The US team is lead by White House Deputy Chief of Staff Joe Hagin, who has served in every Republican administration since Ronald Reagan's presidency.
The two teams met at the luxurious Capella hotel on the island of Sentosa. Some members of the US and North Koreans teams dressed casually in kakis and short sleeve button downs in Singapore's muggy 29 degree heat. The hotel has barred journalists from entering, and a Washington Post reporter was ordered to leave the property after he spoke briefly to the American delegation.
As Hagin entered a meeting with Kim Chang Son, he told the Post that the teams were still discussing the venue for the summit. "We're workin' at it," he said.
The organisers have plenty of options.
The Shangri-La, a 747-room hotel, has hosted major security conferences for years, including the annual Shangri La Dialogue, which attracts dozens of ministers of defence and state, including top US officials.
The Marina Bay Sands hotel and casino, a massive three-towered property with a giant swimming pool atop it, could appeal to Trump's Vegas-style sensibilities, but also poses a conflict of interest. The resort is owned by a company chaired by Sheldon Adelson, one of Trump's biggest political donors, a prospect that could make it more or less appealing.
"Do you help your largest donor or avoid the swamp effect of doing so?" said Douglas Paal, an Asia expert at the Carnegie Endowment for International Peace.
Singapore, as a destination for the summit, has benefits and drawbacks. It's viewed as a neutral city because the island has a long-standing trade and investment ties with the United States and has sustained a diplomatic relationship with North Korea since 1975 while other countries have severed ties. But it won't offer the type of familiarity that benefited the meeting last month between South Korean President Moon Jae In and Kim on the two country's border.
"The South Koreans literally did a dress rehearsal for April 27 at Panmunjom together with North Korean officials a couple of days prior to the event, but that is presumably not an option in Singapore, so there is a lot of stage direction and protocol that will have to be worked through to satisfy both sides," said Scott Snyder, an Asia expert at the Council on Foreign Relations.
"They will have to agree on a minute-by-minute ticktock outlining the course of the entire encounter, including security, media and logistics."
Meanwhile, a separate team of US and North Korean negotiators in the Korean demilitarised zone appears to have hit obstacles following a four-hour meeting. That group is focused on the substance of the negotiations should a Trump-Kim summit happen, but South Korean Unification Minister Cho Myoung Gyon said the different positions of Washington and Pyongyang "remain quite significant."
"It will not be easy to narrow the gap and find common ground, but I think it would not be impossible," he said during an address in Seoul.
The discussions are expected to resume as a separate meeting is set to take place this week between US Secretary of State Mike Pompeo and North Korean official Kim Yong Chol.
Both levels of negotiations between US and North Korean officials are aimed at closing the gap on the issue of North Korea's nuclear weapons programme ahead of the potential summit.
Cho said he remains hopeful for the meeting between Pompeo and Kim Yong Chol, slated to take place later this week.
"Now that the leaders of the two countries are engaging in talks in a top-down manner, I think the chances are high that common ground can be found," he said.
