"He is progressing satisfactorily at this early stage", the palace added in a statement Wednesday. "He is comfortable and in good spirits".
Prince Philip retired from 65 years of public service in August 2017, more than five years after the palace first said he would gradually "wind down" his workload, though he remained keen to carry out many of his duties.
The aging royal did not attend Easter services with the Queen over the weekend because he was having problems with his hip.
Scarlett McNally, an orthopaedic surgeon and council member of the Royal College of Surgeons, said fitness was more important than age when it came to recovering from surgery.
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