The confirmation from Pyongyang directly, rather than from third countries like South Korea, has created more confidence within Trump's administration about the wisdom of holding such a meeting, as US officials make secretive preparations.
White House officials have said North Korea must commit to dismantling its nuclear program and ending weapons testing in order for talks to be productive.
Until now, the US had relied mostly on ally South Korea's assurance of Mr. Kim's intentions. Last year, Trump threatened to bring "fire and fury" on Kim's country if it continued its nuclear weapons and ballistic missile tests.
Trump also confirmed, for the first time, that preparatory talks for the summit are under way between Washington and Pyongyang.
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. "They've said so, we've said so, hopefully it'll be a relationship that's much different than it's been for many, many years".
"We've been in touch with North Korea; we'll be meeting with them sometime in May or early June", Trump told reporters before a Cabinet meeting Monday.
Kim In-kyung has this report.
Citing multiple government sources from North and South Korea, Japanese newspaper Asahi Shimbun reports that Mr Kim was asked: "How about stopping smoking?"
A North Korean diplomat reaffirmed Tuesday that Pyongyang remains committed to denuclearizing the peninsula through progressive and simultaneous actions.
It has not been revealed what North Korea is hoping to achieve at the end of the bilateral talks.
It was Kim's first known trip outside the North since he assumed power in late 2011.
Chung Eui-yong, the director of the South Korean National Security Council, advised Kim Jong Un to stop smoking during a conversation.
The meeting of the Political Bureau of the C.C. came two days ahead of the Sixth Session of the 13th Supreme People's Assembly of the DPRK, slated to take place on Wednesday.
Mongolia's capital Ulaanbaatar is also considered as one of the possible locations, the report added.