Spokespeople for the palaces of King Charles and Prince William declined to comment on the report.
William and Harry, the sons of King Charles, were once seen as very close after the death of their mother Diana in a Paris car crash in 1997.
But they have fallen out in recent years. Since Harry and Meghan stepped down from royal duties two years ago and moved to California they have delivered stinging criticism of the British monarchy and accusations of racism, accusations that the family has dismissed.
According to the Guardian, the dispute with William arose over the royal family's displeasure with Meghan, Harry wrote.
Harry says William called Meghan "difficult," "rude" and "abrasive," which he said sounded like "the press narrative" about Meghan.
Harry has made numerous public statements that both he and his wife were mistreated by the palace and its staff, and accused palace insiders of planting negative stories in the press.
The title of the book "Spare" comes from an oft-cited quote in British aristocratic circles about the need for an heir, and a spare. According to the Guardian, Harry attributes to his father, King Charles as saying on the day he was born to his mother, Princess Diana: "Wonderful! Now you've given me an heir and a spare – my work is done."
The book also recounts "intensely private scenes and conversations," the Guardian reported, such as describing his memories and love of his late mother, who was killed in a 1997 car crash, and grandmother Queen Elizabeth, who died last year at age 96.
Harry and Meghan were married in 2018. They soon grew distant from the rest of the royal family, announcing in 2020 they would "step back" from royal duties, moving to California later that year.
