Kim and President Donald Trump have engaged in an increasingly sharp war of words as North Korea's weapons programs advance, each of them belittling the other.
Trump claimed credit Wednesday for the inter-Korean dialogue, saying North Korea was feeling the pressure of a US -led campaign of sanctions over its nuclear weapons and missile development.
"I don't want to comment on it", Trump told The Wall Street Journal after he was asked directly if he had spoken with Kim.
But North Korean leader Kim Jong Un has shown no sign of willingness to give in to US demands and negotiate away a weapons program he sees as vital to his survival, so any reduction in tensions could prove shortlived. I could give you 20 examples.
In recent days, in a series of media leaks, US officials have spoken of the president's willingness to consider a limited preemptive strike on North Korea to change Kim's mindset, despite the risk of touching off a war. "I'm not saying I have or I haven't".
Kim has warned the United States that he intends to build a nuclear arsenal capable of hitting the United States, prompting threats of military action by Washington. In his New Year's address last week, Kim said he has a "nuclear button" that could fire weapons anywhere in the United States, and Trump responded that he has a much bigger and more powerful "nuclear button".
"You'll see that a lot with me", he said. You give me 30. "I'm a very flexible person".
The first formal talks between the North and South in more than two years are set to take place in a border town Tuesday; the rivals are trying to find ways to cooperate on the Winter Olympics that begin next month in the South. On Wednesday, Trump said he didn't expect a war in a White House news conference, and indicated he was pleased by direct talks between Pyongyang and Seoul.