Mr Trump initially enjoyed a handshake that lasted up to ten seconds as they met for the first time outside the Capella hotel on the Singaporean island of Sentosa.
They then stepped inside, sat down on low, colonial-style chairs and shook hands again for the cameras. As Mr Trump withdrew his hand, he gave a short but unmistakable thumbs-up to Mr Kim.
After shaking hands in front of a row of American and North Korean flags, Mr Trump and Mr Kim walked along a colonnade, inside the hotel and up a flight of stairs.
According to a pool report, at 9:06am, they entered the room where they are holding their one-on-one meeting. The translator sat beside Mr Trump.
Asked how he felt in the first minute, Mr Trump responded: “I feel really great. It’s gonna be a great discussion and I think tremendous success. I think it’s gonna be really successful and I think we will have a terrific relationship I have no doubt.”
The North Korean leader, who borrowed a plane from China to fly to Singapore, said without prompting: “Well, it was not easy to get here. The past has placed many obstacles in our way but we overcame all of them and we are here today.”
Mr Trump said it was an honour to be meeting the leader. “Thank you very much, thank you very much,” he said.
Just how Mr Trump’s thumbs-up will be perceived by the wider world was not immediately. Phil Robertson, deputy director of Human Rights Watch’s Asia division, said it was wrong the US president to do anything that appeared to endorse the head of a regime with such an appalling record on human rights.
The point was all the more prescient, given that the US had said it would not raise the issue of human rights with Mr Kim.
“The problem is that Donald Trump should not be doing anything that looks like it’s an endorsement of Kim Jong-un and the brutal regime he leads,” Mr Robertson, who is Singapore, told The Independent.
“It’s one thing to be talking about denuclearisation and trying to move forward the peace process. But it’s another to be giving the impression you are endorsing the leader of a country with one of the worst human rights records in the world.”
Mr Trump started the talks sounding optimistic about his ability to persuade North Korea to abandon its nuclear weapons programme after a lengthy one-on-one meeting with Mr Kim.
Mr Trump said on Tuesday morning at the beginning of expanded discussions with aides from both countries that “We will solve a big problem” and “a big dilemma”.
According to the Associated Press, he talked about the pair achieving “tremendous success together” and predicted that “it will be successful. It will be done”.