Mr Trump had said on Saturday he would know within a minute of meeting Mr Kim whether he would reach a deal. "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!"
Trump said the process of denuclearisation would happen " very, very quickly", adding that he had formed a "special bond" with Kim and the relationship with North Korea would be very different.
"North Korea's not going to change the way they do business unless they believe that the military option's on the table", Graham, R-S.C., said on "Sunday Morning Futures".
The summit marked the first between a sitting US president and a North Korean leader.
"And if we're not willing to do that, we're not going to get a good deal", Graham said, complementing the worldwide community - including China and Russian Federation - for standing behind Trump in regards to sanctions on North Korea. That is, experts suggest Pyongyang may only agree to give up its nukes in exchange for the USA terminating its military presence in South Korea and ending its regional nuclear umbrella, a security arrangement in which Washington promises in-kind retaliation on behalf of close allies if they are attacked with nuclear weapons.
After greeting each other, the two leaders planned to sit for a one-on-one meeting that a United States official, speaking on condition of anonymity, said could last up to two hours, with only translators joining them.
Donald Trump then guided Kim Jong-un to the library where the one-on-one meeting was to take place.
2008 ‘America’s Got Talent’ victor Neal Boyd dead at age 42
Last year, Neal and his mother were involved in a near-fatal vehicle accident after he blacked out while driving. He was also very involved in politics and campaigned for a Missouri District 149 House Seat in 2014.
"This guy wants to be around the world, he wants to come to America, he wants to enjoy his life, he wants his people to enjoy this life", Rodman said, adding that Mr Kim is "not a dumb man". On a larger level, the astronomical cost of the nuclear weapons program contributes to the massive poverty in North Korea, among the world's poorest countries.
The two posed for pictures briefly before walking over to an awning and appeared quite cordial in their greeting, both smiling as they shook hands for a second time.
For Mr Trump, he's likely to credit any success in these talks to his "maximum pressure campaign".
The US has offered North Korea "unique" security guarantees to persuade it to give up its nuclear arsenal, Secretary of State Mike Pompeo said on Monday, on the eve of a historic summit in Singapore.
Bringing U.S. troops home from North Korea was "not a part of the equation right now", Mr. Trump said when asked for specifics about what he had agreed to.
Top members of Trump's administration have said that the North Koreans wouldn't receive any benefits before taking steps to denuclearize - wary of falling into the same predicament that doomed previous agreements with the rogue regime.
Singapore's Ministry of Foreign Affairs (MFA) released a statement saying the two discussed mutual relations and the situation on the Korean peninsula, with Prime Minister Lee thanking Kim for his and Trump's "bold and admirable decision" to hold the summit.