The two men walked towards each other and firmly gripped each other's hands in front of US and North Korean flags.
Mr Trump patted Mr Kim's arm as they stood on red carpet and exchanged a few words before turning to face the gathered press.
"I feel really great. We're going to have a great discussion and will be tremendously successful," the US president said.
Sitting alongside each other, ahead of a one-on-one meeting, the pair appeared relaxed against the odds.
"It was not easy to get here," Mr Kim said. "There were obstacles but we overcame them to be here," and his counterpart responded "That's true."
The two men, accompanied only by interpreters, spoke for a little under 40 minutes. They were then joined by small delegations of advisors for a working lunch.
From Washington the group included US Secretary of State Mike Pompeo and security adviser John Bolton, and on Pyongyang's side, Mr Kim's "right-hand man" and former spy chief Kim Yong-chol, and foreign minister Ri Yong-ho.
Over lunch they shared a mix of Western and Korean dishes, including stuffed cucumbers and Daegu jorim, a soy-braised fish dish.