Others say that with Singapore being ruled by one family for nearly 60 years, its economic transformation over the years offers a model for a strong developing state.
"That would be a discussion between two democracies: The Republic of Korea and the United States", Mattis told reporters on Monday.
Trump added that he has "no doubt" that the two leaders will have a terrific relationship.
The North Korean leader went on an unannounced late-night sightseeing stroll of the city Sunday, even stopping at one point for a selfie. Trump appeared to be speaking to Kim throughout the 12 seconds of the handshake but Kim did not reply.
Neither man smiled as they walked towards each other and grasped each others hand and then turned towards the cameras.
The stakes remain dizzyingly high and the developments are likely to come rapid-fire.
Last week, Trump told reporters that it would be easy to tell if a deal was possible with Kim in the first minute of the meeting. Following the initial greeting, Trump and Kim will participate in a one-on-one meeting, with translators only, an expanded bilateral meeting, and a working lunch.
"Meetings between staffs and representatives are going well and quickly. but in the end, that doesn't matter", he said.
The White House did not immediately respond to questions about the call. The moves defused immediate threats of military action by the US.
Talks begin between the two leaders and their wider staff
Trump and Kim are expected to discuss North Korea's nuclear weapons and ballistic missiles programs, but the president has cautioned that the summit is meant to mark the beginning of a dialogue between the two countries rather than the conclusion of negotiations.
Pompeo spoke to journalists Monday evening, calling the summit "truly a mission of peace" and saying that the US president is "going into this meeting with confidence, a positive attitude and eagerness for real progress".
Investors spent most of Monday waiting for Tuesday's meeting between Mr Trump and Kim, aimed at settling a standoff over the North's nuclear arsenal.
According to the North Korea news agency (KCNA), the discussions would focus on "the issue of building a permanent and durable peace-keeping mechanism on the Korean peninsula, the issue of realizing the denuclearization of the Korean peninsula and other issues of mutual concern".
It said China plays an "indispensable" role in helping North Korea join the worldwide community and could also help the North open up its economy.
If successful, the meeting would lower geopolitical tensions in an area that involves three of the world's largest economies: South Korea, Japan and China.
The summit is a product of months of diplomacy, going back to the meeting between Kim and South Korean President Moon Jae-in at the end of March.
Despite his young age - officially unknown but believed to be 34 -, Kim has stamped his authority on the North Korean leadership, reportedly undertaking a purge of top officials, including his powerful uncle Jang Song Thaek in December 2013 and the armed forces chief Hyon Yong Chol in April 2017.
How likely is a breakthrough agreement?
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