The president also said he would "absolutely" invite Kim to the White House soon. "If we say we need to fundamentally change the relationship, then you have a framework where there can be real progress".
Critics of the summit leapt at the handshake and the moonlight stroll Kim took Monday night along the glittering Singapore waterfront, saying it was further evidence that Trump was helping legitimize Kim on the world stage as an equal of the US president.
As U.S. President Donald Trump and North Korean leader Kim Jong Un meet on Singapore's Sentosa Island on Tuesday, Trump's Twitter timeline shows an interesting history between the two leaders - one that's marred by insults and threats, with the odd compliment in between.
He went on to say that the current detente between the nations, "probably would not have happened" if it weren't for the case of USA student Otto Warmbier, who died shortly after being flown back to the United States after being held in North Korean detention.
Trump said over the weekend that he would know if Kim is serious about brokering peace within "a minute" of meeting him.
Inside, they sat alongside each other against a backdrop of North Korean and USA flags, with Kim beaming broadly as the US president gave him a thumbs up.
When Singaporean Prime Minister Lee Hsien Loong visited the worldwide media center for the summit at F1 Pit Building on Sunday, he said it will cost the city state "around 20 million Singaporean dollars" (W16.1 billion, US$1=W1,078) to host the "historic summit".
From there, the two will engage in more talks with advisers joining them through a working lunch.
"It was not an easy journey", Kim said, speaking through a translator.
Still, the sense of anticipation was great in Singapore, with people lining spotless streets holding cellphones high as Trump headed to meet Lee.
With a handshake, the leaders of the U.S. and North Korea broke through decades of antagonism, signaling a willingness to stake their reputations on forging a new relationship between the two nations.
After the the one-on-one meeting, Trump did appear to be in a good mood, telling reporters that the private discussion between the two leaders was "very, very good".
"We are hopeful this summit will have set the conditions for future successful talks", Pompeo said yesterday evening.
Pompeo spoke as top officials from the two countries continued negotiations in Singapore ahead of the meeting between Trump and Kim.
CNN has not seen the document, but Trump said it would be shared later that day.
It was not immediately clear what specific progress, if any, had been made in preliminary discussions between United States and North Korean officials. His public statements and state-run media indicate he wants a deal to ease sanctions, but that he won't give up his nuclear weapons until he feels safe enough to retain power without them.
"North Korea has previously confirmed to us its willingness to denuclearize, and we are eager to see if those words prove honest", Pompeo said.
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.
Pompeo laid out some of the US cards on Monday, saying the administration was sticking to its demand for the complete, verifiable and irreversible denuclearization of the North.
Yet the top USA diplomat added Trump is ready to offer "unique" guarantees to ease the regime's concerns about giving up a nuclear arsenal that provides a deterrent against foreign adversaries while also serving as a key point of national pride.
Breaking from the less-than-desired No. 1 post, Smith gunned Justify to the lead and never looked back. More importantly, to his owners at least, the win makes him the most valuable horse in racing history.
Federation Internationale de Football Association 19 has swiped the Champions League license from Rivals Konami and PES. There will be "a few surprises", too It wouldn't be E3 without a couple of big announcements coming out of left field.
He also singled out tariffs on U.S. dairy products in yet another scathing tweet directed at Canada just before the meeting. Canada and Mexico, the other members of the 1994 pact, have been frustrated by the slow pace of talks to renegotiate NAFTA.
This suggestion probably should have a "Kids, do not try this at home" caution, because you know that's what people will do. At the pickup event, customers tested the flamethrowers (which are definitely flamethrowers) by torching marshmallows.
Former prime minister Brian Mulroney predicts Donald Trump's unprecedented diatribe against Justin Trudeau is a passing storm. All seven leaders had worked out a joint statement stressing the importance of a rules-based worldwide trading system.
He went out of his way to be cordial during two summits with South Korean President Moon Jae-in in April and May. Sanctions on North Korea would remain in place until that happened, Pompeo said on Monday.
The flapjack factory launched an advertising campaign Monday touting a $6.99 burger special with unlimited fries and a drink. To learn more about the company's pivot in menu, we got in touch with IHOP's spokesperson, Stephanie Peterson.
Alongside the Final Fantasy, Just Cause 4 , and Tomb Raider announcements, Square Enix revealed a new game called The Quiet Man . This time, however, we were treated to a brand new trailer, and this one reveals the world of Pirates of the Caribbean .
Most Range Rover Evoques and the related Discovery Sport are built at Land Rover's Halewood plant in the United Kingdom , however. The Solihull plant will be converted to manufacture electric and hybrid cars which the company will switch to making from 2020.
Desertion carries maximum penalties of dishonorable discharge, forfeiture of all pay and confinement of five years. Investigators past year caught a fugitive in Florida who had been living under another identity since 1972.
The Division 2 E3 2018 Cinematic Trailer
What's more, Ubisoft said it has "revamped" the Dark Zone PvP mode, though no other details about what's new were shared. More information on The Division 2 is expected to be revealed over the coming week, as E3 2018 kicks off in style.
Thiem steamrolls into maiden grand slam final
But this year's final is already different from any of Nadal's previous 10 in Paris or any of his 13 other Grand Slam finals. Cecchinato's nerves settled and the Sicilian unleashed some trademark backhand winners but Thiem had too much pace and power.
North Korea summit: Human rights not on the agenda
An American reporter asked Trump how he was feeling, followed by a North Korean reporter asking a question to Kim. In Trump's and Kim's meeting on Tuesday, reporters were allowed access for just a few minutes at the beginning.
House vote still looms at Net Neutrality comes to an end
Senate voted to repeal the FCC's decision on killing net neutrality, but this was seen as a largely symbolic victory. The Republican-majority FCC voted along party lines in December to repeal the regulations, which expired today.
The Trump-Kim peace summit has been downgraded to a half-day
They are being housed at the Formula One pit building in the city centre, while Trump stays in the Shangri-La and Kim at the St. He said on Thursday that he didn't think he had to prepare very much for the summit and that "it's about attitude".