"We will all know soon whether or not a real deal, unlike those of the past, can happen!" he wrote.
The meeting was the first between a sitting US president and a North Korean leader.
"She called me and said, 'Dennis, Donald Trump is so proud of you".
He would not say whether that included the possibility of withdrawing U.S. troops from the Korean Peninsula, but said the context of the discussions was "radically different than ever before".
Offering a preview to reporters, Pompeo said it could provide "an unprecedented opportunity to change the trajectory of our relationship and bring peace and prosperity" to North Korea.
Kang Hyung Seok, who is visiting Boston from South Korea, said Monday that whatever the outcome, the meeting itself was encouraging.
Previous attempts to negotiate with Pyongyang have failed, but earlier this year North Korea demonstrated a new openness to diplomacy and held direct talks with Seoul.
North Korea has said it is willing to commit to denuclearisation, but it is unclear how this will be achieved or what might be requested in return.
Aware that the eyes of the world were on a moment many people never expected to see, Kim said many of those watching would think it was a scene from a "science fiction movie".
Advance teams from North Korea and the USA have spent recent weeks in Singapore negotiating everything from presidential hotels to seating charts and lunch breaks during the summit. He had earlier been scheduled to leave on Wednesday.
On Monday morning, the KCNA and the Rodong Sinmun, the official newspaper of the North's ruling party, gave extensive reports on Kim's departure for Singapore and his meetings with Singaporean officials, including its Prime Minister Lee Hsien Loong.
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Critics at home said the joint statement by the two leaders was short on detail and that Trump had made too many concessions to Kim.
His first stop was a park with futuristic, tree-shaped installations, Gardens by the Bay, which also boasts the largest glass greenhouse and tallest indoor waterfall in the world.
The foreign minister posted a selfie of him and a smiling Kim wearing his trademark dark Mao suit on Facebook.
Just a few months ago, Kim was an worldwide pariah accused of ordering the killing of his uncle, a half-brother and scores of officials suspected of disloyalty. The summit with Trump will be another way to win over legitimizing political capital - especially if the summit results in the normalization of U.S.
After meeting privately and with aides, Trump and Kim moved into the luncheon at a long flower-bedecked table.
Rodman told reporters at Changi airport that he'd travelled to Singapore "to see what's going on" and that he hoped "that things turn out to be well for everyone in the world".
The US President is due to meet Kim Jong Un at 9 a.m. local time (9 p.m. ET) outside a luxury hotel here for a handshake before repairing inside for one-on-one talks.
It was a striking about-face from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn scorned the American president as a "mentally deranged USA dotard". "The two leaders discussed recent developments ahead of today's summit with North Korea and agreed to consult closely following the meeting", the Washington's release said on Monday. It heralded the summit as part of a "changed era". The North Korean leader, in his mid-30s, might not have even looked out of place at Marina Bay Sands had it not been for his distinctive striped Mao suit and his massive security entourage.
"He is very talented", Trump said, citing Kim's ability to "take over a situation like he did at 26 years of age and run it, and run it tough". The two will later be joined by officials and have lunch together. In March, Minister of State for External Affairs General V K Singh paid a two-day visit to North Korea, the first ministerial visit from India to North Korea in almost two decades. They believe Kim's engagement is aimed at getting the United States to ease the crippling sanctions that have squeezed the impoverished country.
"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.