Mr Kim also agreed to meet South Korea's president at a tense border village in late April, presidential national security director Chung Eui-yong said after talks with Mr Kim in Pyongyang, North Korea's capital.
North Korean state media said the North and South Korean officials discussed a possible summit between Kim and Moon during a meeting and dinner hosted by Kim on Monday in Pyongyang.
But the US maintained that North Korean gestures of rapprochement would carry little weight without a commitment on nuclear weapons - particularly following last year's nuclear and missile tests carried out by the North.
Moreover, the North said that it "does not have any reason to have nuclear weapons" if there is no hostility or security threat against it. Chung said that the North also made it clear that it would not use its nuclear arsenal or other weapons against the South. "In past negotiations, this has meant that North Korea will only denuclearize if the U.S. and ROK were to end their alliance and the U.S. would remove its military presence on the peninsula".
Japan on Wednesday remained wary of North Korea's agreement with South Korea to hold a summit and its openness to denuclearization talks with the United States, and vowed to keep pressuring the country to abandon its nuclear and missile ambitions.
The first inter-Korean talks in more than two years were held early this year to bring North Korea to the Winter Olympics, when South Korea and the United States also postponed an annual joint large-scale military exercise that North Korea views as a preparation for invasion.
"The key point will be whether Trump will allow any sanctions to be taken off - the most lethal threat North Korea wants to get rid of", said Youngshik Bong, a researcher at Yonsei University's Institute for North Korean Studies in Seoul.
On Tuesday, Trump welcomed Pyongyang's offer as positive, saying the standoff over Pyongyang's weapons drive would not be allowed to "fester".
"The delegation to the North made historic achievements and opened the door for peace on the Korean Peninsula", Back Hye-ryun, the party's spokeswoman, said in her commentary. They just really needed to show re-entry capability to for sure say that they have this capability to attack mainland United States with nuclear-tipped intercontinental ballistic missile. And I think they are spooked by this talk of bloody nose and limited military strike and so on.
"Neither sanctions nor provocations nor threats can ever undermine our position of a nuclear weapons state", it said. "And that should have an effect on North Korea and China". "But. the North Koreans have earned our scepticism, so we're a bit guarded in our optimism". The prospect of a cataclysm that could decimate both North and South, with Trump as instigator, may have convinced both sides to take radical action.
"We know Kim Jong Un, while he's unpredictable, he's also very calculating". For example, the 1994 Agreed Framework got North Korea to freeze its plutonium production for a time, but eventually fell apart during the George W. Bush administration after U.S. intelligence discovered North Korea was secretly pursuing technology for a uranium enrichment program.
In Washington, US intelligence officials said it was too early to assess North Korea's willingness to consider denuclearisation.
But the administration will have difficult questions of its own as it gauges North Korea's intentions. Convincing the U.S.to remove those troops in exchange for promises of denuclearization will probably be a non-starter. The broad list of sanctions envisaged by the law includes various measures, ranging from cutting arms sales and export of sensitive technologies to halting financial assistance and bank loans, none of which seem to be relevant in the case of North Korea, already suffering from multiple rounds of Washington's sanctions.