The Queen has visited Prince Philip in hospital as Buckingham Palace said he is "comfortable and in good spirits" after abdominal surgery.
The duke was said to be "progressing according to plans at this early stage" but will have to rest for two months after the exploratory operation.
Prince Edward visited the London Clinic earlier to see the Duke of Edinburgh, who is celebrating his 92nd birthday.
Asked how his father was, Prince Edward said: "Well, thank you."
The Queen arrived shortly before 1900 BST and spent 30 minutes inside.
In a statement, Buckingham Palace said: "He will remain in hospital for up to two weeks, and it is expected he will then be taking a period of convalescence of approximately two months."
On Monday evening Prince Philip's doctor Professor John Cunningham arrived at the private hospital.
Earlier guns were fired at Edinburgh Castle, London's Green Park, the Tower of London, Cardiff Castle and Hillsborough Castle in County Down, Northern Ireland to mark the duke's birthday.
Officer cadets from City of Edinburgh Universities Officer Training Corps, of which Prince Philip is Honorary Royal Colonel, fired the 21-gun royal salute at Edinburgh Castle.
Lieutenant Colonel Gordon Mackenzie, their commanding officer, said the cadets were "thrilled" to fire the salute in front of large crowds.
Prime Minister David Cameron sent a birthday message to the duke on Twitter, writing: "Wishing the Duke of Edinburgh a very happy 92nd birthday as he recovers in hospital today."
Buckingham Palace said on Friday that the hospital admission had been pre-arranged and was not an emergency.
The duke was admitted on Thursday after a Buckingham Palace garden party, where guests said he had not displayed any signs of being unwell.
He had been having unannounced abdominal investigations at the hospital in the days before.
The results from the exploratory operation are being analysed, and Prince Philip's hospital stay is expected to last about two weeks.
Prince Philip has been admitted to hospital three other times in the past two years after suffering health scares.
In August 2012, he was treated at Aberdeen Royal Infirmary for a bladder infection.
He spent four days in hospital over Christmas 2011, following an operation to clear a blocked heart artery.
After attending events to mark the Queen's Diamond Jubilee in June, he was admitted to hospital for five nights missing several days of festivities after sustaining a bladder infection.