The handshake lasted about 12 seconds.
Trump and Kim have a long day ahead of them.
It's "going to be tremendously successful", Mr. Trump said in introductory comments broadcast live on television.
Kim is due to leave on Tuesday afternoon, a source involved in the planning of his visit has said.
He was overheard telling the US President: "Well, it was not easy to get here".
In the hours before the summit began, Trump expressed optimism about prospects for the first-ever meeting of sitting U.S. and North Korean leaders, while Pompeo injected a note of caution whether Kim would prove to be honest about his willingness to denuclearise.
As I recently wrote, while certain sanctions on North Korea are discretionary, a key 2016 law specifically obligates the president to sanction people and entities complicit in human rights abuses in North Korea - not just those involved in weapons proliferation - and the Trump administration legally can't suspend sanctions more broadly unless North Korea implements key human rights reforms.
Among those joining the leaders on the USA side were Secretary of State Mike Pompeo, White House chief of staff John Kelly and national security adviser John Bolton.
He said the Canadian leader must not have realised that Trump had televisions on Air Force One, allowing him to monitor Trudeau's news conference at the end of the G-7 summit.
"At the conclusion of the summit, President Trump will participate in a media availability before departing tomorrow at approximately 8 p.m. for the United States", the White House said.
The Trump administration seeks a "complete, verifiable and irreversible" dismantlement of Pyongyang's vast nuclear weapons program, which has produced up to 60 nuclear warheads housed across the country, according to U.S. intelligence estimates, as well as a sophisticated program for their delivery worldwide.
Rodman's trip was sponsored by PotCoin, a cryptocurrency company that gives marijuana businesses access to banking as an alternative to many financial institutions that will not do business with cannabis companies because marijuana is illegal under US federal law. Kudlow's wife, Judy, told the Washington Post that "he's doing fine". Very smart, very good negotiator.
Kim stood silently alongside, but the North Korean leader had earlier described their meeting as a "a good prelude to peace".
Breaking down in tears during an interview with CNN's Chris Cuomo, Rodman - known as "The Worm" in his National Basketball Association heyday - recalled, "I said the door would open". "When I went back home, I got so many death threats". I had to hide out for 30 days.
When pressed for a breakdown on the summit expenses, he said, "I think if you calculate the price of everything in this world, you will miss out the really important things".
"I know when somebody wants to deal".
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