Prince Edward, Earl of Wessex, told Sky News his father Prince Philip was "a lot better".
He added: "We've had some brilliant and lovely messages from all sorts of people and we really appreciate that and so does he, I've been passing them on. It's fantastic, thank you."
Prince Philip is likely to stay in hospital for "several days" while he is treated for an infection, Buckingham Palace has said.
The Duke, 99, was admitted to hospital as a "precautionary measure" after feeling unwell seven days ago.
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