South Korea has been keen to lower tensions on the peninsula and some fear that it could bend to Pyongyang's demands.
There had been some suspicion that the meeting might not happen because North Korea still hasn't publicly announced Kim's offer to meet Trump.
This fueled concerns in Washington that Seoul had overstated the North's willingness to negotiate over its own nuclear arsenal, even as officials scrambled to prepare for the prospective meeting. In a growing rapprochement on the Korean peninsula, Kim is scheduled to meet the South's president Moon Jae-in for a rare inter-Korean summit on 27 April.
Trump also talked about the recently renegotiated free trade agreement between South Korea and the USA, saying he think it's going to be "a very fair deal". -North Korea summit would take place by the end of May.
The North Korean leader discussed the "prospect of the DPRK-U.S. dialogue" as well as "strategic and tactical issues to be maintained" by the party, "including the future policy of worldwide relations and the orientation corresponding to them", according to KCNA.
Mr Trump said on Monday that he expected to meet Mr Kim in May or early June, expressing hope that they would reach a deal on "denuking" the Korean peninsula. During previous negotiations under different USA administrations, the North has agreed to freeze its nuclear weapons program in exchange for the lifting of global economic sanctions, only to violate the agreement by testing more weapons.
If the talks go ahead, it would be the first time a sitting U.S. president has met a North Korean leader.
"The pressure is real and has increased, and I do think that it has frustrated Kim Jong Un's ambitions", he said, referring to Kim's "simultaneous push" policy of developing the nuclear program and the economy at the same time. He did not clarify where the session might take place. Secret talks on the specifics are said to be ongoing.
For the better part of past year, North Korea continued to defy worldwide officials' pleas to cease countless nuclear missile and bomb tests, even going so far as to threaten the US territory of Guam after fierce words from Trump demanding a halt to their increased military activity.
Beyond that, a detailed agenda for the talks will need to be set.
That means it wants to see "complete, verifiable, and irreversible" denuclearisation - a very high bar.