Pompeo said the summit should set the framework for "the hard work that will follow", insisting that North Korea had to move toward complete, verifiable and irreversible denuclearisation. "The world will see a major change".
Trump has said he wants to strike a deal to get the North to give up its nuclear weapons.
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. "I also learned that he loves his country very much". Trump has also raised the possibility of further summits and an agreement ending the Korean War by replacing the armistice signed in 1953 with a peace treaty.
At the start of the meeting the American president told the North Korean leader: "Working together we will get it taken care of. we will solve it". Moments earlier, Trump had announced his chief economic adviser, Larry Kudlow, had been sent to the hospital after suffering a heart attack.
The pair made brief remarks as they sat together before the world's media as the historic summit got under way, with the United States leader insisting "we will have a terrific relationship I have no doubt".
"The old prejudices and practices worked as obstacles on our way forward, but we've overcome all of them and we are here today", Kim said.
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".
Trump has downplayed what will come from the meeting, and told reporters last week that it is likely to be just the start. A lot of progress. I think better than anybody could have expected. Top of the line, very good.
The report also said Mr Kim was accompanied by his foreign minister Ri Yong Ho, defence minister No Kwang Chol and sister Ms Kim Yo Jong.
Before signing what Trump described as a "comprehensive" document, Kim said the two leaders had a historic meeting "and chose to leave the past behind".
Reacting to the news of the two leaders meeting, basketball star and unlikely North Korea envoy Dennis Rodman, who is also in Singapore, said holding the summit was the right thing to do.
Despite the comments being largely a repeat of previously expressed concerns by Trudeau, they earned a furious rebuke from both the president and his advisors, who quickly pulled the US away from endorsing a joint statement released by rest of the G-7 allies.
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.
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