When North Korea first threw the fate of a historic summit meeting with the United States into question last week, it cited — five times — the fate of another country and another leader, half a world away, as an example of why no one should trust American efforts to disarm another nation.

The country was Libya, and the leader was Col. Muammar el-Qaddafi, who made a bad bet that he could swap his nascent nuclear program for economic integration with the West. That deal, executed by the Bush administration nearly 15 years ago, is a footnote to American histories of that era.

But Libya has always loomed large for the North Koreans. Mentions of the Libya deal as a model for North Korea’s own denuclearization — first by Mr. Trump’s new national security adviser, John R. Bolton, and then by Vice President Mike Pence — were enough to draw two threats of withdrawal from the talks by North Korea. After the second threat, President Trump announced unexpectedly on Thursday that he had decided to withdraw from the planned June 12 meeting.

Whether Mr. Trump and the North Korean leader, Kim Jong-un, will ever meet — a move disarmament advocates saw as an opportunity to end decades of animosity between the nations — remains an open question.