Trump was joined by Secretary of State Mike Pompeo, National Security Adviser John Bolton, and John Kelly, White House Chief of Staff, for the expanded talks, while Kim's team included former military intelligence chief Kim Yong Chol, foreign minister Ri Yong Ho and Ri Su Yong, vice chairman of the ruling Workers' Party.
Shortly after Trump's presser, a spokesperson from South Korea's Blue House (its executive branch of government) said that "the meaning and intention" of the United States president's remarks regarding the war games "require more clear understanding".
"We will be stopping the war games, which will save us a tremendous amount of money", Trump said during a post-summit news conference.
He refused to go into details. The U.S. would also stop joint military exercises in South Korea.
Pyongyang has demanded the end of what it calls a "hostile policy" towards it, but in public has only pledged to pursue the denuclearisation of the Korean peninsula - a euphemism open to wide differences of interpretation.
The US stations around 30,000 troops in security ally South Korea to protect it from its neighbor, which invaded in 1950 in an attempt to reunify the peninsula by force.
Trump said Tuesday the summit has helped bring the world back from "nuclear catastrophe". He said the U.S. is working on the issue with South Korea, and Japan-as well as with China, but "to a lesser extent".
The result was a nascent diplomatic breakthrough after decades of hostility, but no guarantee that North Korea would follow through.
U.S. President Donald Trump waves next to North Korean leader Kim Jong Un at the Capella Hotel on Sentosa island in Singapore June 12, 2018. "South Korea alliances, then this is the way to launch the process", said Evans Revere, a former USA diplomat in South Korea.
In China, Pompeo's biggest task will nearly certainly be to make sure the government holds up its end of the bargain enforcing the sanctions regime which the US bolstered in recent months and which Trump credits for bringing Kim to the negotiating table.
Trump said verification processes had been discussed at the summit, and that Kim understood it would involve accepting large numbers of USA and worldwide personnel.
This is certainly not the pledge for the unilateral dismantling of North Korea's nuclear programme that the USA has always pushed for.
Trump called the North Korean leader "worthy", "smart" and "talented" after the Singapore summit while days earlier describing Trudeau as "dishonest and weak" following a G7 summit in Quebec.
Mr Trump was asked by reporters during his final appearance with Mr Kim what surprised him most during their meetings. -North Korea relations, and to recover the remains of prisoners of war and military members missing in action.
Many agreements have been made in the past with North Korea that have later fallen apart, and ahead of the meeting, critics expressed concerns that it risked being more about headlines than substantive progress.
The first concrete action was for the American president to announce he intends to call a halt to the annual war game exercises organised between the US and South Korea (the most recent exercises almost derailed the inter-Korea summit a few weeks ago).