Speaking at the White House on Monday, Trump expressed hope that a deal to get Pyongyang to denuclearize might be made.
The report represents DPRK state media's first mention of the date and the place of the upcoming inter-Korean summit. -North Korea contact is proceeding smoothly.
Hearing that the USA has confirmed Kim's willingness to discuss "denuclearization of the Korean Peninsula", however, is far from a surprise.
Mr Trump said on Monday their meeting might be in late May or in June. "They've said so; we've said so".
The communications, still at a preliminary stage, have involved State Department officials talking to North Korea, apparently through its United Nations mission, and intelligence officers from both sides using a separate back channel.
North Korean leader Kim Jong-un chaired a party meeting on Monday, at which he analyzed the future outcome of dialogue with the United States and the development of inter-Korean relations ahead of a summit with South Korea on April 27, state media reports said on Tuesday.
Mr Kim is a notoriously heavy smoker and his former spy chief was reportedly left frozen in terror when Chung Eui-yong, the director of the South Korean National Security Council, told him to consider quitting cigarettes during a conversation over dinner in Pyongyang last month.
Premier Pak Pong Ju, member of the Presidium of the Politburo, also delivered a report on the execution of the 2017 state budget, KCNA reported.
Trump has consistently called for the denuclearization of the Korean peninsula.
It is scheduled to take place without the months of groundwork that usually precedes such meetings.
In South Korea, meanwhile, there are growing signs that Moon Jae-in's government is about to enter its own summit with Kim Jong-un - the third inter-Korean summit later this month - with a different set of assumptions. The Mongolian capital Ulaanbaatar has also been raised as a possible location, the sources said.