In a television documentary to mark 20 years since their mother's death, the princes recall being at Balmoral Castle in Scotland when having what would turn out to be their last telephone call with their mother. They say they were desperate to rush off the telephone and get back to playing instead.
William and Harry, who were 15 and 12 at the time, said they had no notion that the short phone call would be their last with Diana.
Talking about the phone call, his elder brother William said the conversation still weighs on his mind "quite, quite heavily".
"Harry and I were in a desperate rush to say goodbye, you know 'see you later'...If I'd known now obviously what was going to happen, I wouldn't have been so blase about it and everything else," the 35-year-old Duke of Cambridge said.
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The princes said that their mother was a "fun" parent who was a "total kid through and through" and understood the "real life outside of palace walls".
"She was one of the naughtiest parents. She would come and watch us play football and, you know, smuggle sweets into our socks," the 32-year-old British royal said.
Prince William said his mother was "very informal and really enjoyed the laughter and the fun".
Describing her as a "sort of joker", he recalled: "I would be at school and I'd get a card from my mother. Usually she found something, you know, very embarrassing, you know, a very funny card, and then sort of wrote very nice stuff inside."
Unpublished photos of the princes with their mother feature in the programme.
Princes Harry and William are seen looking through Diana's personal album as they talk about how their childhood memories of their mother sat alongside her global image and influence as a campaigner for the homeless, AIDS victims, and banning landmines.
Princess Diana was killed in a car crash in Paris on August 31, 1997.
William said taking part in the programme for ITV network initially seemed "quite daunting" but had been "a healing process as well".