Trump was received by Lee at the presidential palace Istana, where they were expected to discuss everything from the summit preparations to the US' tariff threats.
The meeting was Trump's only scheduled public event today.
Lee also hosted a working lunch for Trump and his delegation.
At the lunch, Trump expressed optimism for tomorrow's meeting with Kim and also thanked his Singapore hosts for their hospitality.
"We have a very interesting meeting in particular tomorrow, and I think things can work out very nicely," he said. "But we appreciate your hospitality and professionalism and your friendship."
Earlier, Trump tweeted it was "great to be in Singapore, excitement is in the air".
Today, Sung Kim, a former US ambassador to South Korea and former nuclear negotiator with the North, will lead a US delegation for a working group with a North Korean delegation at the Ritz Carlton hotel, Sanders said.
"We are also planning a briefing by senior administration officials in the filing centre at the JW Marriott tentatively scheduled for 5 pm local time," she said in the briefing note issued in Washington yesterday.
He thanked Singapore's organisation of the summit as if it was "their own family affair".
The two leaders discussed bilateral relations as well as the summit and the recent positive developments on the Korean peninsula.
Lee complimented the bold and admirable decision by Kim and Trump to come together for the Summit.
Prime Minister Lee wished Kim a success for the summit and expressed hope that the US-North Korea meeting will advance the prospects for peace and stability in the Korean peninsula and the larger region.
Singapore is one of the few countries that have diplomatic relations with both the US and North Korea.
The summit will be the first meeting between Trump and Kim and mark a turnaround of relations between the two leaders after a long-running exchange of furious threats and insults.
The two leaders have had an extraordinary up-and-down relationship over the past 18 months.
Some 2,500 journalists are reporting on the event, which is costing Singapore government about SGD 20 million.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)