Diana died in a 1997 car crash in Paris alongside boyfriend Dodi Fayed. An inquest last year returned a verdict of unlawful killing, blaming the chauffeur's driving and pursuing paparazzi photographers.
The future king's heartfelt comments came as he became patron of The Child Bereavement Charity, which Diana supported.
"Losing a close family member is one of the hardest experiences that anyone can ever endure," he said. "Never being able to say the word 'mummy' again in your life sounds like a small thing.
"However, for many, including me, it's now really just a word -- hollow and evoking only memories.
"I can therefore wholeheartedly relate to the Mother's Day campaign as I too have felt -- and still feel -- the emptiness on such a day as Mother's Day."
The charity is launching a Mother's Day campaign asking people to remember how hard the date can be for children who have lost mothers, or mothers who have lost children.
William, who is second in line to the throne after his father, Diana's former husband Prince Charles, is training to become a search and rescue helicopter pilot in Britain's Royal Air Force.
Media speculation is growing that he could announce his engagement to long-term girlfriend Kate Middleton, who he met while studying at Saint Andrews University in Scotland.
Mother's Day in Britain is marked on March 22.
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