Mr Trump was received by Mr Lee at the Istana, and was accompanied by secretary of state Mike Pompeo, national security adviser John Bolton, White House press secretary Sarah Huckabee Sanders and White House chief of staff John Kelly.
Mr Lee is also hosting a working lunch for Mr Trump and his delegation.
Mr Trump’s motorcade left the Shangri-La Hotel, where he is staying, shortly before noon to make the short journey to the Istana. Crowds of curious onlookers lined the convoy’s route, taking photographs and waving.
Mr Trump also waved to the crowds who lined the streets.
Earlier on Monday morning, Mr Trump tweeted saying it was “great to be in Singapore, excitement is in the air”.
The day began with a series of meetings between North Korean and US officials at the Ritz-Carlton hotel, where US envoy Sung Kim met with high-ranking North Korean diplomats.
Mr Trump, who arrived in Singapore on Sunday evening, was due to meet with US embassy officials later on Monday afternoon.
Mr Trump had cut short his time at the G7 summit in Canada to come to Singapore for the Tuesday meeting with Mr Kim, which will be held at Sentosa’s Capella hotel.
The unprecedented meeting, which is the first time a sitting US president meets a North Korean leader, could see North Korea dismantle its nuclear arsenal in return for economic help and security guarantees.
Mr Lee also held a separate meeting at the Istana with Mr Kim on Sunday. During the meeting, Mr Lee and Mr Kim discussed Singapore-North Korea relations, as well as developments in the North and the region.
Mr Lee also complimented the bold and admirable decision by Mr Kim and Mr Trump to come together for Tuesday’s summit.
More than 2,500 journalists from around the world have converged on Singapore to cover the landmark summit.