The historic summit between U.S. President Donald Trump and North Korean leader Kim Jong Un began with handshakes, smiles and a thumbs up.

After the pair spoke privately with only their interpreters, Trump and Kim walked side-by-side through the Capella Hotel in Singapore before re-entering the meeting room, where they were joined by their most senior officials.

Kim was heard telling Trump through a translator: "I think the entire world is watching this moment. Many people in the world will think of this as a scene from a fantasy...science fiction movie."

Asked by a reporter how the meeting was going, Trump said: "Very good. Very, very good. Good relationship."

Kim also sounded positive about the prospects.

"We overcame all kinds of skepticism and speculations about this summit and I believe that this is good for the peace," he said.

Just a few months ago, Kim was an international pariah accused of ordering the killing of his uncle, a half-brother and scores of officials suspected of disloyalty.

The summit was part of a "changed era", North Korea's state-run KCNA news agency said in its first comments on the event.

Talks would focus on "the issue of building a permanent and durable peace-keeping mechanism on the Korean peninsula, the issue of realising the denuclearisation of the Korean peninsula and other issues of mutual concern," it added.

Ahead of the summit, North Korea rejected unilateral nuclear disarmament, and KCNA's reference to denuclearisation of the peninsula has historically meant it wants the United States to remove a "nuclear umbrella" protecting South Korea and Japan.