President Donald Trump says 'it's an honor' to be meeting with Kim Jong-un, whom he expects to have 'a terrific relationship' with now that they've been personally introduced.

'I feel really great. I feel really great,' Trump told reporters as he sat down for a meeting with Kim devoid of policy officials and only their translators. 'We’re going to have a great discussion, and I think a tremendous success. It's gonna be be tremendously successful. And it’s an honor, and we will have a terrific relationship, I have no doubt.'

Kim told the U.S. president, 'It was not easy to get here...old prejudices and practices worked as obstacles on our way forward, but we overcame all of them.'

'I think that's true,' Trump replied, shaking his counterpart's hand and making what appeared to be joke that was audible to only the two men and their translators as reporters were led out out of the room.

Trump and Kim then held private talks with only their translators for some 45 minutes before walking together along a route that provided them with another opportunity to speak to press.

'Very, very good. Excellent relationship,' Trump told a tightly-restricted group of assembled journalists.

The U.S. president ignored a question from a member of the media on denuclearization.

Moments later, Trump and Kim rejoined senior officials from both nations for a meeting that would get into the nitty-gritty of a possible nuclear disarmament deal.

'Of course there will be challenges ahead but I am ready to listen,' Kim told the U.S. president in the group setting, through a translator.

Trump told him, 'We will solve [this]. We will be successful. And I look forward to working on it with you. It will be done.'

In their very first greeting, Trump set the tone for the talks, sending Kim an outstretched hand and patting the dictator's right elbow with the other. Neither man smiled during the formal photo, taken on a red carpet in front of alternating American and North Korean flags.

As they turned the corner to head into their first set of talks, however, in an area that Trump may have thought was off camera, the U.S. leader broke into a smile as he exchanged quiet words with Kim and another handshake that lasted several seconds.

A third grip-and-grin followed brief remarks to press inside the portion of their one-on-one meeting that was open to cameras. (Daily Mail)