Kim smiled broadly at the meeting today.
Kim told Lee: “The entire world is watching the historic summit between the DPRK and the United States of America, and thanks to your sincere efforts … we were able to complete the preparation for the historic summit.
Trump arrived later on Sunday from the Canadian city of Quebec, where he attended a G7 summit with other world leaders.
He is also set to meet Lee on Monday.
The Trump-Kim summit, which will be held at the Capella hotel on Tuesday, will mark the first time a North Korean leader has met a sitting US president.
The talks will focus on reaching an agreement on the denuclearisation of North Korea in exchange for the easing of economic and diplomatic sanctions.
As he departed on Saturday, Trump said he was on a “mission of peace” but also warned that the face-to-face talks were a “one-time shot.”
“I feel confident Kim Jong-un wants to do something great for his people,” Trump said, adding that, “he won’t have this opportunity again.”
At stake at the summit are North Korea’s nuclear weapons and peace on the Korean Peninsula.
North Korea spent decades developing nuclear weapons, culminating in the test of a thermonuclear device in 2017. It also successfully tested missiles with enough range to reach the US mainland.
The tests came amid a campaign of “maximum pressure,” led by Washington, that tightened economic sanctions against Pyongyang and raised the possibility of military action.
After a flurry of contacts between the two Koreas, South Korean officials suggested to Trump in March that Kim would be willing to meet face-to-face.
The summit comes after weeks of sometimes-contentious discussions and was briefly cancelled amid North Korean outrage over messaging from some US advisers.