The Duke of Edinburgh is into his ninth day in hospital where he is being treated for an infection.
The Earl of Wessex said Philip is “a lot better” as it was announced the 99-year-old would spend several more days at King Edward VII’s hospital in central London.
Edward said his father was “looking forward to getting out” and the family were keeping their “fingers crossed”.
The duke was admitted last Tuesday evening as a precautionary measure after feeling unwell, and walked into the building unaided.
At the time, Buckingham Palace did not disclose the reason for the duke’s admission to the private hospital, but have now revealed he is being treated for an infection and is “comfortable”.
The earl, who said he has spoken to his father on the phone, suggested the duke, who is known for his “no fuss” attitude, was a little frustrated at remaining in hospital and he had been passing on “brilliant and lovely” messages from well-wishers.
Buckingham Palace said in a statement on Tuesday: “The Duke of Edinburgh remains at King Edward VII’s Hospital where he is receiving medical attention for an infection.
“He is comfortable and responding to treatment but is not expected to leave hospital for several days.”
Edward was asked about his father by Sky News’ royal correspondent Rhiannon Mills, while the broadcaster was filming a separate interview with the earl at his Bagshot Park home in Surrey.
He replied: “He’s a lot better, thank you very much indeed, and he’s looking forward to getting out, which is the most positive thing, so we keep our fingers crossed.”
Asked whether Philip was frustrated to be in hospital, Edward laughed and replied: “Just a bit.
“I think that gets to all of us, and then you can only watch the clock so many times and the walls are only so interesting.
“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.”
Philip was initially due to spend a few days under medical care for “observation and rest” but on Friday sources told the PA news agency the duke, who turns 100 in June, was likely to remain in hospital into this week.
Sources have told PA that Philip’s doctor is “acting with an abundance of caution”.