He continued: "But in the end, that doesn't matter".
"The process could be doomed before it begins", said Kelsey Davenport of the Arms Control Association, adding that a common understanding of denuclearisation was key to success.
The president is now in Singapore, just hours away from his historic meeting with Kim.
Pompeo said Monday the only acceptable outcome of the summit is "complete, verifiable and irreversible denuclearization" or dismantlement.
They only ever met with former US presidents, a symptom of six decades of hostility between the USA and North Korea, which remains a pariah in the eyes of the West not just for its nuclear and missile threats but for flouting global norms of diplomatic behavior.
Rodman has consistently described him as his "friend", and his descriptions of the North Korean leader are generally sympathetic. "And we have developed a very special bond", Trump said at the conclusion of the landmark summit.
Throughout the day, Trump and Kim's body language was openly friendly, a striking warmth given Kim's iron grip on power and dismal record on human rights. We both are going to do something.
The talks will focus on North Korea's controversial nuclear programme. Trump appeared to be speaking to Kim throughout the 12 seconds of the handshake but Kim did not reply. China, South Korea, and Russian Federation have all tried to influence the strong-headed leaders before they sit down together for the first time.
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Kim was cheered by onlookers who caught sight of the dictator, who until earlier this spring was not believed to have ever left North Korea as supreme leader.
Although gaps remain over what denuclearisation would entail, Trump sounded a positive note in a lunch meeting with Singapore's Prime Minister Lee.
Getting there won't be easy as long as North Korea remains under the weight of United Nations sanctions.
Trump said, "It's my honor - we will have a terrific relationship, no doubt". But he thinks that his upbringing in America and his exposure to American media made him skeptical about North Korea and the summit.
Mr Trump famously vowed to unleash "fire and fury" if Pyongyang kept threatening the US. After meeting privately and with aides, Trump and Kim moved into the luncheon at a long flower-bedecked table.
"I don't know if the highest-level dignitary is heading to Singapore via China, but security along the North Korea-China border has been a lot tighter since June 8", he said, referring to Kim Jong Un. The duo then moved into a roughly 40-minute one-on-one meeting, joined only by their interpreters, before including their advisers for additional talks.
Relatives of Japanese people abducted by North Korea in the 1970s and 1980s said Monday that the summit between the leaders of the United States and North Korea in Singapore presents a now-or-never opportunity for the return of their loved ones.
The US wants North Korea to get rid of its nuclear weapons in an irreversible manner that can be verified by the global community.
"Working together, we'll get it taken care of", Trump said.
Former U.S. National Basketball Association star Dennis Rodman arrived in Singapore late on Monday for the summit, saying he was "excited to be part of it", although there has been no indication he would be involved in any official talks.