The meeting on Tuesday between the USA president and North Korea's leader, unthinkable until recent months and uncertain until June 1, is a high-stakes and politically risky venture into summit diplomacy by two unpredictable personalities who have famously exchanged personal insults and threats of war.
The almost four-hour summit went "better than anybody could have expected", Trump said; he claimed "a lot of progress", but did not elaborate.
"I feel that Kim Jong Un wants to do something great for his people", Trump said at a press conference in Canada before departing the G-7 summit for Singapore.
"We will get it done", Mr Trump told his much-younger counterpart, referring to cooperation between the two countries. The North Korean leader was educated at a boarding school in Switzerland, where he studied English as well as taking instruction in German, although his grades were reportedlyless than stellar, according to Vanity Fair.
Aware that the eyes of the world were on a moment that many people never expected to ever see, Kim remarked that many of those watching "will think of this as a scene from a fantasy ... science fiction movie".
It was a day of pleasantries, but little public substance.
Robert King, who served as United States envoy on North Korean human-rights issues under the Obama administration, said Trump has used human rights as an instrument to get Kim Jong Un to negotiate on nuclear weapons, but not as a policy priority in its own right.
"It's fantastic, when I said those things, when I said those damn things, when I went back home I got so many death threats", a tearful Rodman told CNN's Chris Cuomo while wearing a "Make America Great Again" hat.
SAUL LOEB, This content is subject to copyright. Trump then directed Kim to walk down a hallway, where they briefly spoke.
Trump made the comments as he and Kim walked together along balcony as they headed to a larger meeting with aides.
It also has two presidential suites, so Trump and Kim won't have to duke it out over who gets the big room.
Many analysts have suggested that the discussion about denuclearization means very different things to North Koreans than it does to American officials. "We will be fine!" This contrasted with Kim, who had comparatively less to lose, having already scored a major win through Trump's agreement to meet him. For North Korea, who has long sought legitimacy on the worldwide stage, the meeting was a historic opportunity to show that it carries weight.
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But there is established precedent for presidents meeting privately with foreign leaders - including foes - with only interpreters. The summit took place at a resort hotel on Sentosa island, just off the Singapore mainland. This week, the president said he looked forward to getting to know his new negotiating partner.
The Trump administration seeks the complete, verifiable and irreversible dismantling of the North's nuclear weapons program. It's a price they are willing to pay for peace.
At one point, Trump suggested to reporters the talks could extend to a second or even a third day if they were going well. It's where former Chinese President Hu Jin Tao stayed during the 2009 APEC Summit (and don't tell Trump, but Hillary Clinton stayed there in 2011, too).
Described by his critics as a mini-Stalin, Kim has been on something of a charm offensive in Singapore since arriving Sunday.
Kim referred to the decades of hostility that preceded the landmark meeting.
But it's Kim's pursuit of nuclear weapons that gives his meeting with Trump such high stakes. "He said: Can you do that".
Kim smiled as he heard the translator interpret the president's remarks, before weighing in with a brief statement of his own. That could lead to misunderstandings, he said, if there are no witnesses to record what is said.
Kim and his regime have made no secret that nuclear weapons are the key to North Korea's survival yet Mr Trump has made equally clear that he will not tolerate the development of a deadly arsenal that could strike the USA mainland.
Addressing reporters on Monday, U.S. Secretary of State Mike Pompeo sought to keep expectations in check, saying: "We are hopeful this summit will have set the conditions for future successful talks".
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