In excerpts published by the Daily Mail on Thursday, the book - Swan Song: Diana, My Sister - the Earl spoke of how Charles' phone call following the car crash in 1997 "all sounded strangely matter-of-fact".
One passage read: "Unlike my other callers, who were stunned, barely able to articulate their condolences and offers of help, he sounded giddily elated - like a lottery winner, I remember thinking at the time.
"He let me know he had informed William and Harry of their mother's death, first thing that morning, in their bedrooms at Balmoral.
"It all sounded strangely matter-of-fact, given the enormity of the disaster.
"Looking back now, I suspect the prince's first reaction must have been to think more of how this event might free him to marry the woman he loved, rather than appreciating the loss of one he did not."
The palace hit back at claims in the memoir with a short statement, saying "the pain of fraternal grief can cloud reason".
Commenting after the excerpts were published on Wednesday, a palace spokesman said: "While we do not comment on books as a matter of principle, His Majesty is mindful that the pain of fraternal grief can cloud reason, affect judgment and colour memory in ways others do not recognise, even many years after such a loss."
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