That mirage of victory was pierced when Fox News called Arizona for former Vice President Joseph R. Biden Jr. at 11:20 p.m., with just 73 percent of the state’s vote counted.

Mr. Trump and his advisers erupted at the news. If it was true that Arizona was lost, it would call into doubt on any claim of victory the president might be able to make.

What ensued for Mr. Trump was a night of angry calls to Republican governors and advice from campaign aides that he ignored, leading to a middle-of-the-night presidential briefing in which he made a reckless and unsubstantiated string of remarks about the democratic process. Standing in the East Room at 2:30 a.m., he dismissed the election as a “fraud” and claimed he wanted to stop the counting of votes and leave the results to the Supreme Court.