Before the start of the private meeting, Trump and Kim exchanged small talk in front of news photographers and television cameras, saying "We look forward to working this out together".
He lionised Trump for achieving "a feat that no one else has ever delivered", adding Kim would also be remembered as "a leader who made a historic moment by taking the first bold step toward the world".
DPRK stands for North Korea's formal name, the Democratic People's Republic of Korea.
Trump said Secretary of State Mike Pompeo would meet with a senior North Korean official next week to continue discussions.
"The greatest achievement of the summit was that Trump's comments show his confidence in resolving any issues [with Kim]", Nam said in a brief meeting with a small group of reporters in Singapore. President Moon Jae-in's office said it needed to analyze the exact meaning of Trump's comments.
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The announcement took South Korean officials by surprise.
"If we end the "named exercises" and shift to a routine training regimen of a winter and summer training cycle - just as the North Korean People's Army conducts - in which we can conduct sufficient training, that will ensure readiness of the combined forces then we will be OK", he said.
"The sanctions will come off when we are sure that the nukes are no longer a factor", Trump said in Singapore after his summit with Kim.
Gardner, however, maintained, "I think what the vice president said today will continue to clarify what the president had talked about".
Only hours before the summit, Mattis told Pentagon reporters that, as far as he knew, the issue of United States troops in South Korea would not be part of any discussion in Singapore.
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He warned North Korea that only when they agree to complete denuclearization can they expect economic sanctions to lift. North Korea responded shortly after by lashing out at Bolton , saying it could not hide its anger toward him.
"The USFK has received no updated guidance on execution or cessation of training exercises - to include this fall's scheduled Ulchi Freedom Guardian", it said in response to a question from Yonhap News Agency.
"It is also a goal of China's to seek denuclearisation on the Korean peninsula, and without a clear timetable or any specific measures to dismantle nuclear weapons in North Korea, Washington will need Beijing if it wants to apply more pressure to Pyongyang". Outside analysts believe the North objects to the drills because it must spend precious resources on its own war games and troop movements.
"I think it's very provocative".
Former Senator Sam Nunn, co-chairman of the Nuclear Threat Initiative, called the historic summit - the first-ever meeting of sitting US and North Korean leaders - just the "beginning of the beginning" of a long process.
Terminating the 1950-1953 Korean War that ended in an armistice had been discussed another part of means to guarantee North Korea regime security, but this was not included in the agreement.
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