Pompeo had earlier tweeted a photograph at breakfast with ambassador Kim, stating the USA position was unchanged: "We remain committed to the complete, verifiable, irreversible denuclearization of the Korean Peninsula".
Meanwhile, President Trump arrived at Paya Lebar Airbase in Singapore in the evening and was also received there by the country's foreign minister Vivian Balakrishnan.
Shortly after a group of suited North Korean diplomats set out from their Singapore hotel on Monday for talks with USA officials on the eve of a historic summit, a bigger group of North Koreans headed out in summery shirts for some shopping. "To all Americans and the rest of the world I'm honored to call President Trump a friend", he said.
As Trump and Lee sat down for a working lunch at the Istana house, Trump sounded optimistic, telling Lee, "We've got a very interesting meeting in particular tomorrow, and I think things can work out very nicely".
Trump, a former real-estate developer, has approached his meeting with Kim like a business negotiation - with flattery, flashy promises and flexible terms juxtaposed with constant threats to walk away from the table.
Whatever complications may arise after the summit, both sides seem eager to stage a smiling photo of the historic handshake.
A Trump administration official, speaking on condition of anonymity, said the US 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.
Trump's bombshell announcement that he was backing out of the G7 communique, made after he left the summit in Canada early, torpedoed what appeared to be a fragile consensus on the trade dispute between Washington and its top allies.
Image Kim Yo Jong also enjoyed a walkabout in Singapore
In a statement released by the state news agency KCNA, it said the two leaders would discuss a "permanent and durable peace-keeping mechanism" for the Korean Peninsula, the "denuclearisation" of the Korean peninsula and other issues of mutual concern.
"If diplomacy doesn't move in the right direction, sanctions will increase", Secretary of State Mike Pompeo says.
Before flying to Singapore, Mr. Trump was in Canada for the G-7 summit with leaders from Canada, France, Germany, Italy, Japan and the U.K. All seven leaders had worked out a joint statement stressing the importance of a rules-based global trading system.
"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", Mr Kim told Mr Lee through an interpreter.
The Republic is no stranger to hosting historic summits.
If the summit is considered a success, nations that sympathize with the North, such as China, Pyongyang's main trading partner and protector, could decide to lift their own sanctions.
The president has allowed that persuading Kim to abandon North Korea's nuclear weapons program will require more than a single sit-down.
"North Korea has been preparing for this meeting for this meeting for 45 years, " he said.
Trump, who has complained about the cost of those troops, might welcome the opportunity, though a troop withdrawal would also reinforce doubts about America's commitment to the Asia-Pacific region.
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