U.S. Secretary of State Mike Pompeo said there is "enormous potential" for the summit, but lowered expectations that the denuclearization of the Korean Peninsula will happen after one meeting. That evening, he said in a tweet that "great progress" was already being made and that denuclearization - "not just a freeze" - was on the table.
Asked by a reporter how he felt about the summit, Mr Trump said: "Very good".
North Korea has said it is willing to commit to denuclearisation, but that term is open to interpretation.
"If diplomacy doesn't move in the right direction, sanctions will increase", Pompeo said.
The US president successfully sought to tighten United Nations sanctions on the North, and to get its traditional ally, China, to go along.
Those points were echoed in Monday's media coverage in North Korea, which stressed that the talks with Trump would focus on forging a relationship more in tune with what was described as changing times - most likely meaning the North's new status as a nuclear-armed state - and its desire for a mechanism to ensure lasting peace on the Korean Peninsula and, finally, denuclearisation. He had earlier been scheduled to leave on Wednesday.
"Everybody understands the stakes", Gorka said.
Earlier in May, North Korea, too, had threatened to cancel the meeting in protest against the joint military exercise the U.S. had conducted with South Korea. Kim finished off the night with a walk along a pedestrian bridge near the city's Merlion Park.
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The media reports on the Trump-Kim talks on Monday follow months of only the scantest of coverage, though Kim's summits with South Korea's president, Moon Jae-in, and China's president, Xi Jinping, received large-scale coverage soon after they had ended.
Just a few months ago, Kim was an global pariah accused of ordering the killing of his uncle, a half-brother and scores of officials suspected of disloyalty.
They are expected to enter their meeting room at the same time but through different doors - an important requirement because it avoids the appearance that one leader has arrived first and is waiting for the other.
Singapore will spend about 20 million dollars to host the historic summit between Trump and Kim, Prime Minister Loong revealed.
"I'm very optimistic that we will have a successful outcome from our meetings tomorrow", he said.
Concrete barricades have been erected outside St Regis Singapore hotel which is within the zoned security area.
At the same time, he said, Kim will want to strengthen his relationships with powers such as China and Russian Federation to protect himself if the North does start dismantling the nuclear arsenal that it has long called its "treasured sword".
USA and North Korean officials huddled at the Ritz-Carlton Hotel Monday ahead of the sit-down aimed at resolving a standoff over Pyongyang's nuclear arsenal.
In short, the US wants Kim to agree to give up his atomic weapons. But he rightly points out that Trump "appears more interested in achieving a deal with North Korea than he is in maintaining peace with some of our oldest allies". They believe Kim's engagement is aimed at getting the United States to ease the crippling sanctions that have squeezed the impoverished country.