The consensus for a second summit was also reached during multiple working-level meetings between the two sides, Joongang Ilbo said.
The White House says Trump will address the media on Tuesday at approximately 8 p.m. local time for the United States.
Pompeo spoke to journalists Monday evening, calling the summit "truly a mission of peace" and saying that the USA president is "going into this meeting with confidence, a positive attitude and eagerness for real progress".
"That would be a discussion between two democracies: The Republic of Korea and the United States", Mattis told reporters on Monday.
But critics said the Kim and Trump summit was more style than substance, producing a document short on specifics about the key issue of Pyongyang's atomic weapons. "More will be discussed at a press conference soon", The New Straits Times quoted Trump as saying.
The North Korean leader, who has rarely left his home country since 2011 and is thought to be 34, took in some of the city sights and was cheered by spectators as he arrived to visit the famous Marina Bay Sands hotel.
The president planned to stop in Guam and Hawaii on his way back to Washington.
GETTY KIM JONG-UN North Korea's leader went for a walk around Singapore
And President Trump has plenty of good reasons to put on a good show in Singapore.
It was a rare disclosure of itinerary of Kim's foreign trip.
"Great to be in Singapore, excitement in the air!"
For his own part, Trump said Monday during a meeting with Singapore's prime minister, Lee Hsien Loong, that "We've got a very interesting meeting, in particular, tomorrow, and I just think it's going to work out very nicely".
As he was trying to build a bridge with Mr Kim, he was smashing longtime alliances with Western allies with his abrasive performance at the G7.
Trump was flanked in the larger meeting by chief of staff John Kelly, Secretary of State Mike Pompeo and national security adviser John Bolton.
The Blue House says Moon told him South Koreans will be praying for a "miraculous result".
Drunk girl gets her head stuck in auto tailpipe at music festival
If Dierks Bentley's next country ditty is about getting one's head stuck in a tailpipe, you'll know where he took inspiration. The girl who got stuck was cited for underage drinking - but a photo of her posing with the pipe later emerged on Facebook.