It is North Korean leader Kim Jong-un's "fixed will" that a summit with US President Donald Trump in Singapore should go ahead, state media say.
Mr Trump cancelled the summit on Thursday, citing the North's "hostility", but then rowed back after conciliatory messages from Pyongyang.
Late on Saturday he again said the 12 June date for talks "hasn't changed".
Leaders of North and South Korea have also agreed to "meet frequently", the North's KCNA agency added.
It follows a surprise summit between Mr Kim and Moon Jae-in on Saturday.
President Moon's spokesman said there had been a "candid" exchange of views in the two hours of talks between the two leaders.
Their second-ever meeting took place in the demilitarised zone between the two countries. It appeared to be an effort to put the proposed US-North Korea summit back on track.
"They shared the opinion that they would meet frequently in the future to make dialogue brisk and pool wisdom and efforts, expressing their stand to make joint efforts for the denuclearisation of the Korean peninsula," KCNA said.
It said Kim Jong-un had thanked Moon Jae-in for "much effort made by him" to arrange the Singapore summit and "expressed his fixed will" that it would take place.
The statement added that Mr Kim and Mr Moon had agreed to hold further high-level talks on Friday but no details were given.
The White House confirmed on Saturday that an advance team of officials would leave for Singapore this weekend, as originally scheduled, to prepare for the possible summit.
Mr Trump took to Twitter on Saturday to angrily dismiss media speculation that the summit, even if reinstated, could not now be held in Singapore in the existing time frame.
He declared the summit cancelled on Thursday, blaming North Korea's "tremendous anger and open hostility", but tweeted on Friday that "very productive talks" had taken place with the North.
"We're gonna see what happens," Mr Trump told reporters at the White House in Washington.
"We're talking to them [North Korea] now. It was a very nice statement they put out."
He was referring to comments from the North's Vice-Foreign Minister, Kim Kye-gwan, who said that Mr Trump's decision was "unexpected" and "extremely regrettable", adding that Pyongyang was willing "to sit face to face at any time".
Mr Trump had left the door open by saying in a letter to Mr Kim that "wonderful dialogue" had recently taken place and that he was still looking forward to meeting the North Korean leader.
Saturday's surprise talks were held on the northern side of the Panmunjom truce village, between 15:00 and 17:00 local time (06:00 and 08:00 GMT), Mr Moon's office said.
In a brief statement afterwards, South Korea said both leaders had "exchanged opinions... for the successful holding of the North Korea-US summit".
The US is demanding that North Korea completely end its nuclear weapons programme.
North Korea has conducted six nuclear tests since 2006 and numerous tests of intercontinental ballistic missiles that could, theoretically, reach the US. However, experts have cast doubt on whether the North is capable yet of creating a nuclear warhead for a missile.
North Korea has been subjected to numerous rounds of international sanctions since 2006, which has cut off most of its exports and capped its imports of oil.
Experts believe that economic pressure brought about by the sanctions has encouraged Kim Jong-un to seek talks.