"If diplomacy doesn't move in the right direction, sanctions will increase", Secretary of State Mike Pompeo says.
Wearing a marijuana cryptocurrency t-shirt, dark sunglasses, and a "Make America Great Again" hat, Rodman told CNN he is "just happy to be a part of it because I think I deserve it".
The summit included a 38-minute one-on-one meeting where only Kim, Trump and their translators were in the room.
It is the first time a sitting United States president has ever met a North Korean leader.
Trump also reaffirmed the tight US-Singapore relations by reassuring PM Lee that he was "his friend".
"Well, it was not easy to get here", Kim said through an interpreter, before noting the two were able to overcome "obstacles" to start the summit. On a larger level, the astronomical cost of the nuclear weapons program contributes to the massive poverty in North Korea, among the world's poorest countries.
"I feel really great".
The two posed for pictures briefly before walking over to an awning and appeared quite cordial in their greeting, both smiling as they shook hands for a second time. Kim is seeking a security guarantee - and possibly a peace treaty - and the removal of the U.S.'s nuclear umbrella protecting allies South Korea and Japan.
In the run-up to the talks, Trump had hopefully predicted the two men might strike a nuclear deal or forge a formal end to the Korean War in the course of a single meeting or over several days. But no one can credibly suggest that a durable or verifiable denuclearization of the Korean peninsula can be achieved when North Korea remains a completely closed and totalitarian state.
While Trump and Kim search each other's eyes and words for signs of trust or deceit, the rest of the world will be watching, hoping that somehow these two unpredictable leaders can find a way to defuse one of the planet's most unsafe flashpoints.
Setting out the USA position before the summit, Pompeo stressed that the Trump administration would only accept complete denuclearisation of the North.
One of the world's most reclusive leaders, Kim visited Singapore's waterfront on Monday, smiling and waving to onlookers, adding to a more affable image that has emerged since his April summit with South Korean leader Moon Jae-in.
Yet the top USA diplomat added Trump is ready to offer "unique" guarantees to ease the regime's concerns about giving up a nuclear arsenal that provides a deterrent against foreign adversaries while also serving as a key point of national pride.