Trump said on Thursday he is open to meeting Kim again, but in his speech on Friday, the North Korean leader said the outcome in Hanoi led him to question the strategy he embraced a year ago of global engagement and economic development.
The comments comes just one day after Mr Trump, at the start of talks in Washington with South Korean President Moon Jae-in, floated the possibility of further meetings with Mr Kim. While hailing his relationship with Trump, Kim also said the US has been making "gangster-like" unilateral demands and should abandon that approach.
"If [the United States] keeps thinking that way, it will never be able to move the DPRK even a knuckle nor gain any interests no matter how many times it may sit for talks with the DPRK", Kim said, according to a transcript published by the state-owned Korean Central News Agency.
"A third Summit would be good in that we fully understand where we each stand", the USA president said in a pair of Saturday morning tweets.
But Jackson said there was no sign Kim was willing to make the nuclear concessions demanded by Trump's "uber-hawks", implying that the summit-driven process will continue to drag out without bringing nuclear stability to the Korean Peninsula.
In the Oval Office the U.S. president said: "We will be discussing that and potential meetings, further meetings with North Korea and Kim Jong-un".
"As President Trump has repeatedly mentioned, personal relations between me and President Trump are not as hostile as relations between the two countries, and we still maintain excellent relations and can exchange letters whenever we would like to", Kim said.
Last month, Vice Foreign Minister Choe Sun-hui accused the U.S. of taking a "gangster-like" stance and said they had thrown away a "golden opportunity" in Hanoi.
Analysts viewed Friday's announcements as the biggest shake-up in North Korean government in years, a consolidation of power that clearly separated Kim Jong-un's regime from that of his father for the first time.
Said Mr Kim Hyun-wook, a professor at the Korean National Diplomatic Academy: "They want to see the U.S. make the next move - that the steps that they took, such as returning war remains and shutting down missile sites, are even more grounds to demand the United States to relieve sanctions".
"North Korea has tremendous potential for extraordinary growth, economic success and riches under the leadership of Chairman Kim".
South Korea's Blue House said in a statement that officials would "do what we can in order to maintain the current momentum for dialogue and help negotiations between the USA and North Korea resume at an early date".
Responding to Mr Kim's speech, South Korea repeated its stance of promoting the talks.
"By that sort of thinking, the USA will not be able to move us one iota even if they sat with us a hundred, thousand times, and will not be able to get what it wants at all", he said.
But the lack of substantial disarmament commitments from the North and the deepening impasse in nuclear negotiations have fueled doubts over whether Kim would ever voluntarily relinquish an arsenal he may see as his strongest guarantee of survival. But North Korea for decades has been pushing a concept of denuclearization that bears no resemblance to the American definition, with Pyongyang vowing to pursue nuclear development until the United States removes its troops and the nuclear umbrella defending South Korea and Japan.