The reported agreement, if confirmed by the United States, could be considered as a concession by Trump because US officials had called for the North to take swift disarmament measures before getting major outside concessions and benefits.
And money - especially the way Trump thinks the rest of the world takes advantage of the U.S. - was a theme the USA president returned to repeatedly in the post-summit press conference.
"Trump, he has to make the agenda on the table about North Korean human rights", he said in a telephone interview.
"We overcame all kinds of skepticism and speculations about this summit", Kim said, "and I believe that this is good prelude for peace". But I think without the rhetoric - other administrations, I don't want to get specific on that, but they had a policy of silence.
Speaking later, the prime minister struck a noticeably more upbeat tone.
Kim said that the "world will see a major change" and he and Trump "decided to leave the past behind" as they put pen to paper.
"It's going to be a lot different than it was in the past", Trump concurred.
Trump's diplomacy "sends all the wrong messages to China, North Korea and Russian Federation", said Malcolm Davis, a senior analyst at the Australian Strategic Policy Institute. "There were obstacles but we overcame them to be here". "You know, he can have a membership at Trump National", Graham said on CBS, referring to Trump's golf course. "The other approaches haven't worked".
No official announcement has yet to be made about whether North Korea made an agreement concerning nuclear testing or research, as Trump mentioned in his tweet.
Those conditions were absent from the wording of the joint declaration. "To me the conjoining or the return to one another is a very, very necessary path to ultimate healing for that peninsula".
Bishop said Australia had already offered its services with regards to denuclearisation "because we have expertise in that regard".
The account Wednesday in the official Rodong Sinmun newspaper could signal the first rift with President Trump over the perceived path forward with the North's leader, Kim Jong Un.
The report said the historic meeting marked a "radical switchover" in the two nations' fraught relations that had "lingered for the longest period on the earth". "North Korea ends up BACKTRACKING on previous promises on denuclearization".
"We would like to seek an understanding of this between Japan, the USA and South Korea", Onodera was quoted as saying.
Now a top analyst with United States Institute of Peace, Mr. Yun told CNN on Tuesday that halting joint U.S.
Conservative House Republicans were unrepentant in their praise for the president for engaging with North Korea, a sharp reversal from many of their views on similar negotiations between President Barack Obama's Secretary of State John Kerry and Iran.
"Well, he is very talented", Mr Trump said.
The drills - often called "war games" - are held in South Korea with local forces and USA soldiers stationed there.
The US would suspend "provocative" war games it holds with South Korea.
Japan would continue joint military exercises with the USA and would stick to plans to bolster its defences against a possible ballistic missile strike from North Korea.
Trump and Kim met in Singapore on Tuesday for their countries' first-ever summit talks.
The result was a nascent diplomatic breakthrough after decades of hostility, but no guarantee that North Korea would follow through.
North Korea blamed botulism and ingestion of a sleeping pill and dismissed torture claims.