"We hope North Korea and the United States will be able to hold discussions based on mutual respect and understanding", said Eugene Lee, the ministry's spokeswoman.
The meeting was kicking off at 9 a.m. Tuesday with a handshake between Trump and Kim.
Trump responded to such commentary on Twitter, saying: "The fact that I am having a meeting is a major loss for the US, say the haters & losers".
He would not say whether that included the possibility of withdrawing US troops from the Korean Peninsula, but said the USA was "prepared to take what will be security assurances that are different, unique, than America's been willing to provide previously".
In June 1994, former U.S. President Jimmy Carter travelled to North Korea via the DMZ and had two rounds of lengthy talks with Kim Il Sung in an effort to resolve an early round of nuclear confrontation.
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The Worm has visited North Korea on multiple occasions and competed on Celebrity Apprentice in 2013.
The Wonsan Special Tourist Zone in the east coast, or the suspended inter-Korean factory park in the North's border city of Kaesong are some other examples Kim might pursue to maintain state controls over the economy, experts say. It will be the first meeting between a sitting US president and a DPRK top leader.
Lee complimented the bold and admirable decision by Kim and Trump to come together for the Summit.
After meeting privately and with aides, Trump and Kim moved into the luncheon at a long flower-bedecked table.
"The entire world is watching the historic summit between [North Korea] and the United States of America, and thanks to your honest efforts. we were able to complete the preparations for the historic summit", Kim told Lee through an interpreter.
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A Trump administration official, speaking on condition of anonymity, said the USA side was entering the talks with a sense of optimism and an equal dose of scepticism given North Korea's long history of developing nuclear weapons. 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. "Why would Kim. believe any commitments President Trump makes when he arbitrarily tears up an agreement with which the other party is complying?" said Antony Blinken, who was deputy secretary of state under Barack Obama.
Though it could mean many things, the relative speed of the reports about Kim traveling to Singapore could be seen as a sign of confidence by the North that the summit will go well.
But some question why Kim should trust any guarantees given Trump's history of pulling out of accords - most recently the painstakingly negotiated Iran nuclear deal.
Under Kim, Pyongyang has made rapid progress in its weapons technology, carrying out by far its most powerful nuclear test to date past year and launching missiles capable of reaching the USA mainland.
The JoongAng Ilbo said North Korea and the United States, when their officials met in NY and elsewhere to prepare for Tuesday's Trump-Kim summit in Singapore, also agreed on the need for additional summits.
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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 arrived later in the day from a fraught G7 meeting with world leaders in Canada. He has also raised the possibility of further summits.