Trump is set to meet Kim on Tuesday morning in Singapore.
In the run-up to the meeting, Trump had 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.
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The first-ever meeting between a sitting United States president and a North Korean leader is to kick off at 9 a.m. Tuesday at Capella Hotel on the resort island of Sentosa in Singapore.
Trump has also said he'd consider inviting Kim to Washington for a second round of talks.
The two clasped hands for a long while Tuesday as they posed for photos in front of a row of USA and North Korean flags.
In 2014, Trump tweeted dismissively about the possibility that he and Rodman would someday travel to North Korea together. The outcome, of course, would still be that US goal of complete denuclearization.
Sanctions on North Korea would remain in place until that happened, Pompeo said. "If diplomacy does not move in the right direction. those measures will increase".
North Korean Kim Jong-un and President Donald Trump are preparing for a June 12th nuclear summit in Singapore. He was originally scheduled to leave on Wednesday. But the White House said he will instead leave at about 8pm on Tuesday - nearly 15 hours earlier.
So in the evening, his motorcade started moving, and he ended up stopping by a botanical garden called Gardens by the Bay and then taking a selfie there with the foreign minister for Singapore, and then moved on to the Marina Bay Sands, the iconic three-tower hotel in Singapore itself.
Singapore was "clean and beautiful", Kim said on the observation deck, adding that he aimed to learn from the knowledge and experience of the southeast Asian nation, as he found it impressive, the official KCNA news agency added.
At their summit in April Kim and South Korean President Moon Jae-in agreed to seek a peace treaty and Trump mused earlier this month: "Can you believe we're talking about the ending of the Korean War?"
Just a few months ago, Kim was an worldwide pariah accused of ordering the killing of his uncle, a half-brother and scores of officials suspected of disloyalty.
Officials of the two sides held last-minute talks to lay the groundwork for the summit of the old foes, an event nearly unthinkable just months ago, when they were exchanging insults and threats that raised fears of war.
The 45-minute talk between Trump and Kim was held privately.
Rodman told reporters at Changi airport that he'd travelled to Singapore "to see what's going on" and that he hoped "that things turn out to be well for everyone in the world".
As his summit with U.S. President Donald Trump nears, Kim has reason to be nervous. "I could see Trump giving up a lot for very little in return". But there were scant details on what new commitments had been secured from Kim, even as Trump announced he would end the regular military exercises the U.S. conducts with South Korea.
It is not known who has been translating for Mr Trump at the Sentosa Hotel in Singapore. It heralded the summit as part of a "changed era".
It reported that the discussions are going to focus on "the issue of building a permanent and durable peacekeeping mechanism on the Korean peninsula, the issue of realising the denuclearisation of the Korean peninsula, and other issues of mutual concern". She also led a large North Korean art troupe sent to South Korea during the February Winter Olympics in Pyeongchang. In 1948, reunification negotiations failed between North Korea and South Korea, and separate governments were formed, with Kim Il Sung being chosen as the first supreme leader of North Korea.
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