By Agence France-Presse
Seoul had earlier announced the two Koreas would hold a historic summit in the Demilitarized Zone next month -- and that the North's leader Kim Jong Un was ready to halt provocative missile and nuclear tests and sit down with its old enemies.
North Korea's reclusive leader was further said to be willing to consider the dramatic step of abandoning costly and controversial weapons of mass destruction programs if the United States agrees not to attack or overthrow the regime.
Although Trump's response was positive, his administration followed it up with another sharp rebuke when it declared that it had formally concluded that Kim's regime had last year murdered his half-brother in a Malaysian airport with the banned VX nerve agent.
Trump also sounded a note of warning, signaling the threat of military action remains on the table should talks fail to make headway, and his administration said it would press ahead with potentially provocative joint war games with South Korea.
But the US leader was upbeat on the news from Seoul, crediting Washington's "very, very strong" sanctions push, as well as "big help" from China, for the potential diplomatic breakthrough.
Calling the statements coming out of both Seoul and Pyongyang "very positive," Trump refused to rule out a historic meeting with Kim.
"We have come a long way at least rhetorically with North Korea," Trump said.
"We are going to do something, one way or the other, we are going to do something and not let that situation fester."
North Korea's talks offer appeared to be "sincere," he said, adding: "We'll soon find out."
United Nations Secretary-General Antonio Guterres urged all sides to seize the opportunity presented by the talks to move toward "sustainable peace and denuclearization."
The United States says Pyongyang is testing -- and will soon complete -- an intercontinental ballistic missile capable of delivering a nuke to the continental United States.
That ominous technological breakthrough would put cities like Los Angeles and even New York in striking distance of a hostile regime, something that is unthinkable to many in the West Wing.
And Washington said its finding that Pyongyang was responsible for the February 2017 assassination of Kim Jong Nam, Kim's elder half-brother and a potential rival, by spraying VX in his face at a busy Malaysian airport underlined the danger.
"This public display of contempt for universal norms against chemical weapons use further demonstrates the reckless nature of North Korea and underscores that we cannot afford to tolerate a North Korean WMD program of any kind," State Department spokeswoman Heather Nauert said.
Under the US legal ban on chemical weapons, the formal finding triggers a new layer of US economic sanctions, but in practical terms these duplicate those already in place.
- Neighborhood diplomacy -
The apparent offer of talks, not yet publicly confirmed by North Korea, is a tantalizing one for the White House -- offering a possible off-ramp from the road to a bloody war. But it is also fraught with risks.
On multiple occasions, Kim's father Kim Jong Il dangled the prospect of talks and denuclearization as a means of buying time, easing sanctions and dividing South Korea from its allies.
South Korea has been deeply worried by the bellicose rhetoric coming from both Kim and Trump, and has jumped at an Olympic-fueled diplomatic opening.
Next month's summit -- the result of a series of meetings on either side of the contested border -- would follow a year of high tensions during which Pyongyang carried out its most powerful nuclear test to date, along with launches of rockets capable of reaching the US mainland.
Trump has dubbed Kim "Little Rocket Man" and boasted about the size of his nuclear button, while the North Korean leader called the American president a "mentally deranged US dotard."
But the Pyeongchang Winter Olympics in the South triggered an apparent transformation, with Kim sending his sister to the opening ceremony, sparking a flurry of cross-border trips as South Korean President Moon Jae-in moved to broker talks between Pyongyang and Washington.
Kim Yo Jong's visit to the South was the first by a member of the North's ruling dynasty since the end of the 1950-53 Korean War.
North and South agreed to hold a summit in late April in Panmunjom, the truce village in the DMZ, South Korea's national security adviser Chung Eui-yong said after leading the most senior delegation to travel North for more than a decade.
- 'Very important breakthrough' -
It will be the third meeting between the leaders of the two Koreas, but the first to take place in the DMZ after summits in Pyongyang in 2000 and 2007.
The North "made clear that there is no reason to own nuclear (weapons) if military threats toward the North are cleared and the safety of its regime is guaranteed," Chung said.
Pyongyang "expressed willingness to have frank dialogue with the US to discuss the denuclearization issue and to normalize North-US relations," he added, and said there would be no provocations such as nuclear or ballistic missile tests while dialogue was under way.
"Also, the North promised not to use atomic weapons or conventional weapons towards the South," he told reporters, adding that Seoul and Pyongyang would set up a hotline between the leaders.
Kim also said he would "understand" if the South goes ahead with delayed joint military exercises with the US that usually infuriate Pyongyang, a senior official at the South's presidential office added.
Previous negotiations with Pyongyang have ultimately foundered. Six-party talks, grouping the two Koreas, Russia, China, Japan and the US, and offering the North security and economic benefits in exchange for denuclearization, broke down almost a decade ago.