The escalation in the war of words comes after President Donald Trump tweeted Kim Jong Un "won't be around much longer."
North Korean government officials have been quietly trying to arrange talks with Republican-linked analysts in Washington, in an apparent attempt to make sense of President Donald Trump and his confusing messages to Kim Jong Un's regime.
The outreach began before the current eruption of threats between the two leaders, but will likely become only more urgent as Trump and Kim have descended into name-calling that, many analysts worry, sharply increases the chances of potentially catastrophic misunderstandings.
"Their No. 1 concern is Trump. They can't figure him out," said one person with direct knowledge of North Korea's approach to Asia experts with Republican connections.
There is no suggestion that the North Koreans are interested in negotiations about their nuclear program - they instead seem to want forums for insisting on being recognized as a nuclear state - and the Trump administration has made clear it is not interested in talking right now.
At a multilateral meeting here in Switzerland earlier this month, North Korea's representatives were adamant about being recognized as a nuclear weapons state and showed no willingness to even talk about denuclearization.
But to get a better understanding of American intentions, in the absence official diplomatic talks with the U.S. government, North Korea's mission to the United Nations invited Bruce Klingner, a former CIA analyst who is now the Heritage Foundation's top expert on North Korea, to visit Pyongyang for meetings.
Trump has close ties to Heritage, a conservative think-tank which has influenced the president on everything from travel restrictions to defense spending, although not to Klingner personally.
"They're on a new binge of reaching out to American scholars and ex-officials," said Klingner, who declined the North Korean invitation. "While such meetings are useful, if the regime wants to send a clear message, it should reach out directly to the U.S. government."
North Korean intermediaries have also approached Douglas Paal, who served as an Asia expert on the national security councils of Presidents Ronald Reagan and George H.W. Bush, and is now vice president for studies at the Carnegie Endowment for International Peace.
They wanted Paal to arrange talks between North Korean officials and American experts with Republican ties in a neutral place such as Switzerland. He also declined the North Korean request.
"The North Koreans are clearly eager to deliver a message. But I think they're only interested in getting some travel, in getting out of the country for a bit," Paal said.
North Korea currently has about seven such invitations out to organizations that have hosted previous talks - a surprising number of requests for a country that is threatening to launch a nuclear strike on the United States.
Over the past two years in particular, Pyongyang has sent officials from its foreign ministry to hold meetings with Americans - usually former diplomats and think-tankers - in neutral places such as Geneva, Singapore or Kuala Lumpur.
They are referred to as "Track 1.5" talks because they are official (Track 1) on the North Korean side but unofficial (Track 2) on the American side, although the U.S. government is kept informed of the talks.
North Korean leader Kim Jong Un. Photo / AP
But since Trump's election in November, the North Korean representatives have been predominantly interested in figuring out the unconventional president's strategy, according to almost a dozen people involved in the discussions. All asked for anonymity to talk about the sensitive meetings.
Early in Trump's term, the North Koreans had been asking broad questions: Is Trump serious about closing American military bases in South Korea and Japan, as he said on the campaign trail? Might he really send American nuclear weapons back to the southern half of the Korean Peninsula?
But the questions have since become more specific. Why, for instance, are Trump's top officials, notably Defense Secretary Jim Mattis and Secretary of State Rex Tillerson, directly contradicting the president so often?
"The North Koreans are reaching out through various channels and through various counterparts," said Evans Revere, a former State Department official dealing with North Korea who is a frequent participant in such talks. There are a number of theories about why North Korea is doing this.
US President Donald Trump responding to a reporter's question on health care. Photo / AP
"My own guess is that they are somewhat puzzled as to the direction in which the U.S. is going, so they're trying to open up channels to take the pulse in Washington," Revere said. "They haven't seen the U.S. act like this before."
Revere attended a multilateral meeting with North Korean officials in the picturesque Swiss village of Glion earlier this month, together with Ralph Cossa, chairman of the Pacific Forum of the Center for Strategic and International Studies and another frequent interlocutor with Pyongyang's representatives.
The meeting is an annual event organized by the Geneva Center for Security Policy, a government linked think-tank. But it took on extra significance this year due to the sudden rise in tensions between North Korea and the United States.
All the countries involved in the now-defunct six-party denuclearization talks - the U.S., China, Japan, Russia, and the two Koreas - were represented, as were Mongolia, the Swiss government and the European Union. The Swiss invited the U.S. government to send an official, but it did not.
The North Koreans at the meeting displayed an "encyclopedic" knowledge of Trump's tweets, to the extent that they were able to quote them back to the Americans present.
Pyongyang's delegation was headed by Choe Kang Il, deputy director of the Americas division in the foreign ministry, and he was accompanied by three officials in their late 20s who wowed the other participants with their intellectual analysis and their perfect, American-accented English. One even explained to the other delegates how the U.S. Congress works.
"They were as self-confident as I've ever seen them," said Cossa. Revere added: "They may be puzzled about our intentions but they have a very clear set of intentions of their own."
The participants declined to divulge the contents of the discussions as they were off the record.
North Korea's Foreign Minister Ri Yong Ho speaks outside the UN Plaza Hotel, in New York. Photo / AP
But others familiar with the talks said the North Koreans completely ruled out the "freeze for freeze" idea being promoted by China and Russia, in which Pyongyang would freeze its nuclear and missile activities if the United States stopped conducting military exercises in South Korea. The United States, Japan and South Korea also outright reject the idea.
Participants left the day-and-a-half-long meeting with little hope for any improvement any time soon.
"I'm very pessimistic," said Shin Beom-chul, a North Korea expert at the South's Institute of Foreign Affairs and National Security, after participating in the meeting in Glion. "They want to keep their nuclear weapons and they will only return to dialogue after the United States nullifies its 'hostile policy.' They want the U.S. to stop all military exercises and lift all sanctions on them."
Ken Jimbo, who teaches at Keio University in Japan and was also at the meeting, said that North Korea may still be interested in dialogue, but it on terms that are unacceptable to the other side.
"North Korea wants to be recognized as a nuclear weapons state," Jimbo said. "But when is North Korea ready for talks? This is what I kept asking the North Koreans: How much is enough?"
