U.S. President Donald Trump flanked by Secretary of State Mike Pompeo and White House Chief of Staff John Kelly attend a lunch with Singapore's Prime Minister Lee Hsien Loong and officials at the Istana in Singapore, June 11, 2018. "We will be tremendously successful", Trump said before their private session.
Officials remain uncertain what will come out of Tuesday's unprecedented summit, the first of its kind between a sitting US president and the leader of North Korea.
Some critics questioned the pomp surrounding the Singapore summit, saying it unduly elevated North Korea's rogue regime.
Many analysts have suggested that the discussion about denuclearization means very different things to North Koreans than it does to American officials.
Trump said the meetings are going on well.
Rodman spoke from Singapore, where he had traveled to play his part in the summit between the two nations.
In the same statement, the White House said the talks between U.S. and North Korean officials were moving "more quickly than expected", though didn't elaborate on what precisely that meant for Trump's stated goal of securing North Korea's complete and verifiable denuclearization.
Both men looked serious as they got out of their limousines for the summit at the Capella hotel on Singapore's Sentosa, a resort island with luxury hotels, a casino, manmade beaches and a Universal Studios theme park.
The Associated Press reported that while the press corps and White House have an agreement to allow a full pool of reporters into any meetings where media is allowed, reporters for the AP and other outlets were kept out of some events at the Singapore summit.
USA offers 'unique' guarantees to North Korea on eve of summit
From there, the two will engage in more talks with advisers joining them through a working lunch.
Pompeo said the meeting could provide "an unprecedented opportunity to change the trajectory of our relationship and bring peace and prosperity" to North Korea.
Setting out the United States position before the summit, Pompeo stressed that the Trump administration would only accept complete denuclearisation of the North.
But there is established precedent for presidents meeting privately with foreign leaders - including foes - with only interpreters.
A hand from the US President on Mr Kim's arm provided some warmth to an exchange being so closely scrutinised around the world. Past nuclear deals have crumbled over North Korea's reluctance to open its doors to outsiders.
Following an on-camera greeting, the pair will begin the summit with a one-on-one meeting with only their translators, according to a senior Trump administration official.
That is in direct contradiction to a 2014 tweet by Trump, who said Rodman was "delusional" for wanting him to visit North Korea.More news: Halo Infinite Announced by Microsoft!