Pompeo offered "unique" security guarantees to North Korea if it accepts denuclearisation of the Korean Peninsula.
United States President Donald Trump has expressed keenness about his summit with North Korean leader Kim Jong Un while calling it a "one-time opportunity".
"The great risk is that Kim badly botches his meeting with Trump, other North Korean officials seem to be stalling, and the USA delegation gets the sense they are being taken advantage of".
That was an apparent nod to North Korea's sensitivities about the fate of Libyan leader Moammar Gadhafi, who gave up his fledging nuclear program in exchange for economic incentives from the United States only to be ousted and killed by a mob years later.
But when pressed by reporters, the secretary of state would not say whether or not that could include reduction of the number of or removal of USA troops in South Korea. It will certainly be an exciting day and I know that Kim Jong-un will work very hard to do something that has rarely been done before...
In a statement, the White House said Mr Trump would speak to the media before departing for the USA at 8:00pm. Trump plans to brief reporters following the summit's conclusion, and will leave for the USA around 8pm local time (midnight NZT). Find us on Facebook too!
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.
For the North, Kim Jong Un has already won a huge propaganda bonus by merely having the summit and sitting down as an equal with the US president, an accomplishment his father and grandfather sought but could never realize.
"If diplomacy does not move in the right direction.those measures will increase", he said.
North Korea, on May 24 carried out the demolition of its Punggye-ri nuclear test site in a series of "huge" explosions.
Trump and Lee shook hands for photographers after a one-on-one meeting and before they entered the room for lunch. Instead, they are looking for a commitment from Kim to move forward on negotiating the details of a complete and verifiable dismantling of North Korea's nuclear weapons programs. He came and he said 'thank you for hosting and we hope that will be a historic occasion.' I think he wants to go onto a new path.
Although summit meetings between potential enemies are generally a positive indicator for war risks, they are largely symbolic and do not necessarily point to a shift in the conflicting motivations and strategic interests of the countries involved.
Trump and Defense Secretary Jim Mattis have insisted the USA military presence and longstanding alliance with the South is not on the table in talks with the North.
He said Iran views Mr Trump and the United States with "great pessimism", saying they are known for "quitting treaties and violating their commitments".
The lobby of President Donald Trump's hotel in Singapore has turned into a bustling mixing ground for U.S government officials of all stripes.
U.S. secretary of state Mike Pompeo told reporters that ongoing talks between the two countries are advancing well, but stressed the meeting would be the beginning of a process that would "set the conditions for future talks".
Bandow noted that American companies could also turn to North Korea for low-priced manufacturing, which neighbors - like China and South Korea - already benefit from.
Kim arrived at Singapore's Changi Airport after his longest trip overseas as head of state, wearing his trademark dark "Mao suit" and distinctive high-cut hairstyle.