The meeting was the first between a sitting US president and a North Korean leader.
But Trump said, "We could absolutely sign an agreement and we're looking at it", adding, "Sounds a little bit odd, but that's probably the easy part".
The war-like rhetoric these tensions generated made Kim's diplomatic U-turn and the current search for peace - leading to a rash of summits with South Korea and now the United States - all the more surprising. At the same time, he'd admitted he didn't believe he required extensive preparation to take stock of Kim.
President Trump has said the best-case scenario is not going to resolve all these issues.
Joint armed forces of from the Chinese police and the People's Liberation Army have enforced tight security in the border area of Dandong in northeastern China's Liaoning province, that lies across from North Pyongan province, the source told RFA's Korean Service. -North Korean summit before actual procedures for the return are worked out between Japan and North Korea.
MINISTRY OF COMMUNICATIONS AND INFORMATION REPUBLIC OF SINGAPORE HANDOUTKim Jong-un welcomed as he arrives for the summit
But there was no mentioning the previous USA aim of "complete, verifiable and irreversible denuclearization". By contrast, Trump appeared to back off a military footing on Tuesday, declaring the U.S. will stop the "war games", an apparent reference to joint military exercises with South Korea that North Korea has long rebuked as provocative.
"The way coming here was not easy", said Kim.
Kim was cheered by onlookers who caught sight of the dictator, who until earlier this spring was not believed to have ever left North Korea as supreme leader.
South Korea estimates the North has 50 kilogrammes of plutonium, reportedly enough for around 10 bombs, and a "considerable" ability to produce uranium weapons. "If they don't denuclearise, that will not be acceptable", Mr Trump said ahead of the meeting.
Kim is staying at the $9,000-a-night presidential suite at the St. Regis Hotel, while Trump is at the luxurious Shangri-La Hotel.
Senators Move To Reverse Trump's Deal Lifting Sanctions On China's ZTE
Zhongxing Telecommunications Equipment (ZTE) Corporation is a Chinese company headquartered in Shenzhen, Guangdong, China. Commerce Department banned American companies from selling components to ZTE , which also makes smartphones.
A formal end to the Korean war may also be discussed.
Getting there won't be easy as long as North Korea remains under the weight of United Nations sanctions.
Mr Trump famously vowed to unleash "fire and fury" if Pyongyang kept threatening the US.
Trump also said he hopes to eventually withdraw USA forces from South Korea, but said "that's not part of the equation right now". "We just need the doors to be opened so we can start fresh", he said, telling Cuomo, "it's a great day" and exclaiming: "I'm so happy!"
While Trump and Kim shake hands, searching each other's eyes and words for signs of trust or deceit, the rest of the world will be watching, hoping that somehow these two unpredictable leaders can find a way to defuse one of the planet's most unsafe flashpoints. I am optimistic of the outcome of this upcoming summit - a meeting that has the chance to shape global peace and security for decades to come.
November Ballot to Include a Proposition on Breaking California Into Three States
Senate from 100 to 104 members, and the state's 55 electoral points would be divided among the three, according to Ballotpedia. The new California would retain Los Angeles , Ventura, Santa Barbara, San Luis Obispo, Monterey and San Benito counties.
Predicting a tremendous success of the summit with the DPRK leader, Trump said that it was "an honor" to meet face-to-face with Kim and that he would have "a terrific relationship" with the DPRK leader.
The evening tour may have been an attempt to highlight to Kim the economic benefits that could flow - with U.S. support - if Kim agrees to give up his nuclear arsenal.
"We hardly ever talk politics", Rodman said.
While human rights will get a low billing in Singapore, Trump hasn't totally ignored the issue.
Myong Sool Chang, editor of Boston Korea, a weekly newspaper and online news source that covers the Korean community in New England, said that he hopes the summit ends in a deal for North Korea to abandon its nuclear weapons - a development that could bring economic benefits.
Cohen likely to cooperate with federal prosecutors
The source said Cohen had not yet met with prosecutors to speak about a potential deal, and it's unclear whether either side is seeking one.