Addressing the issue last week, Secretary of State Mike Pompeo said he was "confident" that the USA president and the North Korean leader would hold a new meeting to negotiate denuclearisation of the Korean Peninsula "in the coming months".
Telling North Korea's Supreme People's Assembly that USA diplomats came to the last meeting, which ended abruptly in late February with no agreement, without "a clear direction and methodology", Kim had tough words for the Trump administration in his speech Friday.
"If the U.S. adopts a correct posture and comes forward for the third DPRK-U.S. summit with a certain methodology that can be shared with us, we can think of holding one more talks", Kim said.
Despite the heavy criticism aimed towards the US, Chairman Kim indicated he would not hesitate to sign an agreement if the US "stop its current way of calculation and come to us with a new calculation".
"We were informed by the prison authorities that she would be released on May 3, and it is likely she will be flown back to Hanoi on the same date", he said, when contacted.
A Vietnamese woman who had been accused of killing the half-brother of North Korea's leader will be freed from a Malaysian prison on May 3, her lawyer said, a day earlier than previously expected. If the relationship between North Korea and South Korea can be mended, that's a positive development for all concerned, but they can handle that without us.
"As President Trump continues to note, personal relations between myself and President Trump are not as hostile as the relations between our two nations", Kim said.
Kim said he would wait until the end of the year "for the U.S. to make a courageous decision" to change its approach and smooth the path to another meeting, state media reported, after his most recent summit with Trump in Vietnam broke down without agreement.
Kim made the comments during a speech Friday at a session of North Korea's rubber-stamp parliament, which made a slew of personnel changes that bolstered his diplomatic lineup amid stalemated negotiations with the United States.
Mr Trump claimed North Koreans officials wanted all economic sanctions lifted in their entirety in exchange for disabling a major nuclear site, provoking him to walk away. "But it will clearly be hard for a good opportunity like last time to come up".
He also set the United States a deadline of "until the end of this year" to demonstrate that new talks could be more productive.
Since the tense summit, North Korea has threatened to suspend denuclearization talks with the United States.
Jeong Young-tae, an analyst at the Institute of North Korean Studies in Seoul, says the new title is part of Pyongyang's efforts to "secularise" Kim and his power.
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.