North Korea on Thursday called US Vice President Mike Pence "ignorant and stupid" for renewing a threat to cancel the June 12 meeting to be held in Singapore.
The high stakes talks between president DonaldTrump and Mr Kim were to have focused on ridding North Korea of its nuclear weapons and improving ties after decades of animosity.
The summit was scheduled after months of unusually cordial diplomacy between the historic foes, brokered by South Korea.
As part of the reconciliation, North Korea carried out what it says is the demolition of its nuclear test site in the presence of foreign journalists on Thursday, deep in the mountains of the North's sparsely populated northeast.
The North's decision to close the site has generally been seen as a welcome gesture by Mr Kim to set a positive tone ahead of the summit. Even so, it is not an irreversible move and would need to be followed by many more significant measures to meet Mr Trump's demands for denuclearisation.
The North did invite international inspectors to the ceremony, which limits its value as a serious concession.
The newfound bonhomie between the US and North Korea, and the meeting of their leaders, had been thrown into doubt in recent days with both Washington and Pyongyang raising the prospect of cancelling the talks and trading threats.
The latest broadside from North Korea came on Thursday with vice minister of Foreign Affairs Choe Son Hui lambasting a Monday media interview in which Mr Pence warned Mr Kim that it would be a "great mistake" to try and play Mr Trump.
Mr Pence also said North Korea could end up like Libya, whose former leader Muammar Qaddafi was killed by US-backed rebels years after giving up atomic weapons, "if Kim Jong un doesn't make a deal".
"I cannot suppress my surprise at such ignorant and stupid remarks gushing out from the mouth of the US vice president," Ms Choe said in a statement released by the state-run KCNA news agency.
"We will neither beg the US for dialogue nor take the trouble to persuade them if they do not want to sit together with us," she said, adding she would recommend Mr Kim cancel the talks if Washington continued to make such threats.
Similar comments comparing North Korea to Libya from Mr Trump's hawkish National Security Adviser John Bolton caused the first threat by Pyongyang last week to cancel the Singapore meeting.
"Whether the US will meet us at a meeting room or encounter us at nuclear-to-nuclear showdown is entirely dependent upon the decision and behaviour of the United States," Ms Choe added.
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Politically, Trump has invested heavily in the success of the planned summit, and so privately most US officials, as well as outside observers, believe it will go ahead.
Hand-picked aides -- including deputy chief of staff Joe Hagin and deputy national security adviser Mira Ricardel -- are traveling to the Southeast Asian city state designated to host the summit, officials said.
They are expected to meet their North Korean counterparts and iron out details of the meeting.
But Mr Trump has also become increasingly lukewarm about meeting Mr Kim, teasing his commitment to talks as keenly as any of his "The Apprentice" season finales.
"On Singapore we'll see. It could very well happen," he said on Wednesday, adding cryptically: "Whatever it is, we'll know next week."
Mr Trump enthusiastically embraced the idea of talks earlier this year.
But as the date draws nearer, the gulf in expectations between the two sides is coming into sharp relief.
Washington has made it clear it wants to see the "complete, verifiable and irreversible denuclearisation" of the North.
But Pyongyang has vowed it will never give up its nuclear deterrence until it feels safe from what it terms US aggression.
On Wednesday US Secretary of State Mike Pompeo -- who has met personally with Mr Kim -- said whether the summit goes ahead is now up to North Korea. His remarks reflect an effort to perhaps lay the groundwork for blame should the talks fail.
