Singapore is one of the few countries that have diplomatic relations with both the United States and North Korea.
"It's our contribution to an international endeavour which is in our profound interest," Lee told reporters at the huge media centre the city-state had constructed to deal with the enormous demand.
Over 2,500 journalists are covering the summit, the first between a sitting United States President and a North Korean leader.
Lee said the cost of the summit for Singapore was 20 million Singapore dollars.
"It is a cost we are willing to pay," he said, adding that security costs would account for about half of that figure.
The summit has the potential to set developments on the Korean Peninsula on a new path, Lee was quoted as saying by Straits Times newspaper.
The summit is a plus for Singapore, he said.
"It gives us publicity. The fact that we have been chosen as the site of the meeting - we did not ask for it, but we were asked and we agreed - says something about Singapore's relations with the parties, with America, with North Korea, also our standing in the international community," he said.
Meanwhile, North Korean leader Kim met with Singapore Prime Minister Lee, hours after arriving here.
Kim was greeted at Singapore's Changi airport by Singapore's Minister for Foreign Affairs, Vivian Balakrishnan.
Balakrishnan, an Indian-origin politician, had earlier visited Pyongyang and held talks with senior North Korean leaders to tie-up the details of the summit.
According to images released by the Singaporean government, Kim arrived on an Air China plane. Accompanying him was Kim Yong Chol, who earlier this month met with President Trump to hand deliver a letter from Kim.
Trump yesterday declared that the young dictator had a "one-time shot" to bring his country in from the cold with the summit.
President Trump will arrive later today. The US hopes the summit will kick-start a process that eventually sees Kim give up nuclear weapons.
Kim and Trump will sit down for talks at 9 am (6:30 am IST) on Tuesday at the Capella Hotel on the resort island of Sentosa.
Singapore has been used before for high-profile diplomatic occasions. In 2015, the leaders of China and Taiwan held historic talks in the city-state - their first in more than 60 years.