Trump met Prime Minister Lee Hsien Loong on Monday at the city-state's presidential palace Istana, where they were expected to discuss everything from summit preparations to the U.S.'s tariff threats.
Trump has said he hopes to make a legacy-defining deal for the North to give up its nuclear weapons, though he has recently sought to minimize expectations, saying more than one meeting may be necessary.
A USA official says Monday that the leaders will meet for up to two hours before an expanded bilateral meeting with their respective advisers.
Trump on Monday morning broke into a Twitter tirade about trade directed at America's European allies with the upbeat message: "Great to be in Singapore, excitement is in the air!".
Officials who arrived with Trump include Secretary of State Mike Pompeo, National Security Adviser John Bolton, White House Chief of Staff John Kelly and White House Press Secretary Sarah Sanders. It will be the first ever meeting between a sitting US President and North Korean leader. The nation also has repaired ties with China after a setback in late 2016, a shift reinforced by Lee's visit to Beijing in April.
Another Pyongyang report quoting Kim Yong-nam, the nominal head of state, as telling leader Kim to achieve outstanding outcomes from the summit with the USA has also drawn attention.
"If the summit becomes a success, the Singaporean efforts will go down in history", Kim said.
A dispatch by the state-run Korean Central News Agency says Kim and Trump will exchange "wide-ranging and profound views" on establishing a new relationship, the issue of building a "permanent and durable peace mechanism" and realizing the denuclearization of the Korean Peninsula.
"The first minute I'll know - just my touch, my feel, that's what I do", Trump said over the weekend at the G-7 summit in Canada.
Both leaders have arrived in Singapore for their historic meeting.
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.
Prime Minister Lee Hsien Loong announced this on Sunday, adding that the June 12 summit will give Singapore global publicity and demonstrate the country's standing in the worldwide community.
When a couple of guests were seen sneaking a photo, a North Korean official stormed up to them, demanding to check their phones.
Trump flew into Singapore's Paya Lebar Air Base on Sunday aboard Air Force One.
At the hotel lobby, grim-faced North Korean security guards warned other hotel guests not to take pictures as Kim walked to his Mercedes Benz limousine.
A year ago the North carried out what was by far its most powerful nuclear test to date and launched a flurry of missiles - including two over Japan - while Trump threatened Pyongyang with "fire and fury" and Kim dubbed him a "mentally deranged USA dotard".
Ahead of his much-anticipated meeting with Kim, the US President sounded optimistic and said the meeting would be a "one-time shot" at peace.
North Korean leader Kim Jong-un's sister Yo-jong gets into a van at the St. Regis Hotel in Singapore on Sunday.
It is the farthest Kim has travelled since inheriting power in 2011, and only his third known trip outside the country since then, with the use of a Chinese plane raising questions over the state of North Korea's ageing fleet of Soviet-built aircraft.