Citing a White House official, it said, Trump "remains open to engaging with [North Korean leader Kim Jong-un] to achieve a fully denuclearized North Korea."
The response came shortly after Kim's sister, Yo-jong, snubbed Trump's repeated overtures for rapprochement with the isolated country.
In a statement carried by the state-run Korean Central News Agency (KCNA) the same day, she said, "I do not want to deny the fact that the personal relationship between the head of our state and the present U.S. president is not bad."
But she added that if such an attempt is meant to "serve the purpose of denuclearization, it can be interpreted as nothing but a mockery of the other party," rejecting "any attempt to deny the position of [North Korea] as a nuclear weapons state."
Trump, who had a couple of photo ops with Kim during his first term, has claimed on several occasions that he still has a "good relationship" with Kim.
The previous day, she also ruled out any chance of resuming talks with the South, saying that South Korean President Lee Jae-myung is "no different from his predecessor in blindly adhering to the South Korea–U.S. alliance and pursuing confrontation" with the North.
"I make it clear once again that we are not interested in any policy or proposal put forward by Seoul, and there will be no chance of us sitting down with South Korea for any discussions," she fumed.
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