Kim told Lee that if his meeting with Trump is successfully held, Singapore's efforts will be historically recognized, expressing gratitude for the city-state's provision of convenience to the North's delegation.
President Trump and North Korea's Kim Jong Un will start their historic summit with a one-on-one session with only their translators.
Rodman is one of a handful of Westerners to have visited reclusive North Korea and met Kim.
Kim and the Singaporean premier discussed "issues of developing the bilateral relations in an all-round way by invigorating wide-ranging exchange and cooperation while maintaining the excellent relations and deepening the friendly relations between the two countries".
The meeting was Trump's only scheduled public event today.
Previous agreements with the North have subsequently collapsed and experts warn Kim is highly unlikely to give up the "treasured sword" of his nuclear deterrent.
Trump and Kim are staying in separate hotels in the famous Orchard Road area of Singapore, dotted with high-rise luxury apartment blocks, offices and glittering shopping malls. After their initial greeting, the leaders will head into a room for the summit.
The first-ever meeting between a US president and a North Korean leader was to kick off at 9 a.m. Tuesday (9 p.m. EDT Monday in the U.S.) with a handshake, an image sure to be devoured from Washington to Pyongyang and beyond.
The top Democrat on the Senate Foreign Relations Committee says the North Korean leader has already achieved some success just by bringing the American president to the table.
"Thanks PM Lee for spending $20 million of taxpayers money, which can. help a lot of needy families in Singapore to survive", posted one Facebook user.
"[President Trump] is not going to permit any show of weakness on the trip to negotiate with North Korea", Kudlow said on CNN's State of the Union.
The global community hopes that the encounter between Kim and Trump will also contribute to a greater understanding, finish the enforcement of sanctions and allow once and for all to end the crisis that on more than one occasion stoked the fear of a war break in the Korean peninsula. He initially touted the potential for a grand bargain with North Korea to rid itself of a nuclear missile programme that has advanced rapidly to threaten the United States.
It was reported that Kim planned to fly back to North Korea in the early afternoon on Thursday, leaving very little time for actual negotiations, although there is still considerable uncertainty about what a deal between the leaders would look like.