Kim also said he would wait until the end of the year "for the US to make a courageous decision" on another meeting, after his most recent summit with Trump in Vietnam broke down and both sides left without agreement.
"We are willing to give another try if the US offers to have a third summit with the right attitude and mutually acceptable terms," he said, according to a report by North Korean state media outlet KCNA.
Kim added that his personal relationship with Trump remained strong, adding they could "write letters to each other" whenever they wanted.
"We will wait with patience until the end of the year for the US to make a courageous decision," Kim said.
Trump and Kim held their first landmark summit in Singapore last June, where the pair signed a vaguely-worded agreement on the "denuclearisation of the Korean peninsula".
But the failure to reach agreement at their second summit in Hanoi has raised questions over the future of the accord.
Trump said Thursday he was mulling a third summit with Kim ahead of a meeting with his South Korean counterpart Moon Jae-in at the Oval Office -- a move supported by Seoul.
Moon brokered the US-North Korea talks and has been pushing for the resumption of inter-Korean economic projects, but doing so would fall foul of international sanctions imposed on Pyongyang.
"Our government will do what we can in order to maintain the current momentum for dialogue," Moon's office said in a Saturday statement.
The day before Kim accused Seoul of acting as an "overstepping mediator" and said the South should "speak up" for Pyongyang's interests.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)