Tearing up, Rodman said he'd received "death threats" for what he'd said about North Korea.
"We may be able to recoup a little bit of that but I think it is a cost that we're willing to pay and it's our contribution to an worldwide endeavour, which is in our profound interests", said Lee during a press conference held at the summit's global Media Centre.
He talked about the pair achieving "tremendous success together" and predicts that "it will be successful".
For the North, Mr Kim has already won a huge propaganda bonus by merely having the summit and sitting down as an equal with the US President, an accomplishment his father and grandfather sought but could never realise.
The two are due to meet on Tuesday on the resort island of Sentosa for their high-stakes summit, the first-ever talks between the United States and North Korean leader and the culmination of a head-spinning diplomatic dance.
They shook hands for several seconds, Trump reaching out to touch the North Korean leader on his right shoulder.
Singapore's Ministry of Foreign Affairs said in a statement that Mr Kim and Mr Lee discussed relations between their countries, as well as developments in North Korea and the region, including recent positive developments on the Korean peninsula. As a rule, they would only report on the leader's movements after the event.
Flight from Pyongyang lands in Singapore ahead of North Korean leader’s arrival
At 10am, North Korean vice-minister for foreign affairs, Choi Sun-hee, strode into the Ritz Carlton with her small team. Concrete barricades have been erected outside St Regis Singapore hotel which is within the zoned security area.
Professor Hajek added Trump showed his experience in front of the TV cameras during the initial meeting.
Replied the guy who, nine months earlier, compared Trump's speech at the UN General Assembly to the sound of a barking dog: "It has not been easy to come to this point".
The US president left the Shangri-La Hotel, where he is staying, at about 11.45am in a motorcade of more than 30 vehicles.
The two men later emerged from their meeting looking relaxed as they walked the open-air corridors. Then aides to each were to join for more discussions and a working lunch. Trump and Kim are making comments. To some national security veterans, it raised concerns about the risk of holding such a monumental meeting solo.
The relative speed with which state media reported on Kim's arrival suggests a some confidence that the meeting will go well - or at least well enough. He also said that he understands English when he talks about basketball, a sport North Koreans allegedly enjoy. No, no, say others, you need to manage your expectations. "I'll tell you what the Marshall wants more than anything". Pyongyang has advocated for decades for a peace treaty to formally end the Korean War, rather than the armistice that has been in place for more than 60 years.