Spencer writes that then-Prince Charles had told him "we'll forget her soon enough" during an angry phone call after Diana's death, following what he said had been a disagreement over whether her sons Princes William and Harry should walk behind their mother's coffin.
Buckingham Palace took the unusual step to dispute Spencer's account.
Asked about it in a BBC interview, Spencer said: "Those are precisely the words he said."
CHARLES SOUNDED 'GIDDILY ELATED'
In the book, Spencer writes that Charles had sounded "giddily elated" and "like a lottery winner" when he had called him after Diana's death.
Spencer says that he had later suspected Charles may have been thinking about how Diana's death could free him to marry Camilla, now his wife, though he acknowledged in a BBC interview that he could not know for certain what Charles was thinking.
SPENCER OPPOSED WILLIAM AND HARRY WALKING BEHIND COFFIN
Spencer says he had argued against plans for William and Harry, then aged 15 and 12, to walk in Diana's funeral procession through London because he then believed she would not have wanted them subjected to the ordeal.
QUEEN ELIZABETH OFFERED TO RESTORE DIANA'S ROYAL TITLE
Spencer says that Queen Elizabeth, through her private secretary, had offered to posthumously restore Diana's "Her Royal Highness" title on the day of her funeral.
According to the book, Spencer rejected the offer, saying it had come too late.
DIANA CONSIDERED CALLING OFF HER WEDDING TO CHARLES
Spencer writes that his sister had considered ending her engagement to Charles before their 1981 wedding because she feared he did not love her.
He says she had raised her concerns with their father but ultimately proceeded with the marriage.
DIANA HAD THOUGHTS ABOUT SUICIDE
Spencer wrote that "in her later years, Diana drove herself more than once to Beachy Head, the highest chalk sea cliff in England, while contemplating ending it all".
"Her love for her sons stopped her from going further," he said in his book.
WHY SPENCER WROTE THE BOOK
Spencer, 62 and only three years apart from his sister, told the BBC he wrote the memoir because he felt it was his "duty" as an "eyewitness to history" and wanted to record what he believed was a truthful account of Diana's life before the 30th anniversary of her death.
He told the BBC that he knew "lots of things about the King which I chose not to include", saying the book would be his last word on the matter.
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