However, Leong said both found it hard to hide their nervousness once they were seated, with Trump displaying a slanted smile, and fidgeting with his hands and Kim leaning and staring at the ground.
Kim Jong Un and Donald Trump shook hands once again ahead of a private meeting with only their translators present.
Asked by reporters how the talks were going, Mr Trump said: "A lot of progress - really very positive".
"An unsuccessful summit would be one in which talks break down, leading to renewed and heightened tensions, possibly similar to what was seen in 2017 with harsh words and bellicose actions by both sides".
After a handshake, they were soon smiling and holding each other by the arm, before Trump guided Kim to the library where they held a meeting with only their interpreters.
A luxury hotel in Singapore on Tuesday distributed 250 special Trump-Kim burgers with American and Korean taste among public to celebrate the historic summit and allow people to enjoy the friendship while eating.
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.
Accompanying Trump were White House Chief of Staff John Kelly, National Security Advisor John Bolton, and Secretary of State Mike Pompeo.
On the DPRK side, Kim Yong Chol and Ri Su Yong, two vice chairmen of the Workers' Party of Korea (WPK) Central Committee, and Foreign Minister Ri Yong Ho were present.
We wonder whether they were comparing portable toilets because we know Kim Jong-un takes one everywhere.
At the top of the expanded meeting, Trump said he and Kim "will solve" the problems presented by a nuclear North Korea.
But he added: "In the end, that doesn't matter".
Kim said he wanted to express his gratitude to President Trump for making the meeting happen.
In a letter on Monday, Senate Democrats outlined how they believe Trump should handle negotiations with Pyongyang, saying any deal should require that North Korea give up its nuclear and ballistic weapons programs.
Pompeo declined to comment on a question about the approximately 28,500 USA servicemembers based in South Korea. Kudlow's wife, Judy, told the Washington Post that "he's doing fine".
It is the first time a sitting United States president has ever met a North Korean leader. "I just feel, my instinct, my talent", he says.
"It is unbelievable, it is wonderful. when I went back home, I got so many death threats". And I believe North Korea and when I came home, I couldn't even go home. I had to hide out for 30 days.
"Should we keep going Sarah?" We will continue that and I think ultimately agree to something.