Britain's Prince Philip set to stay in hospital into next week
The Duke of Edinburgh, as he is formally known, is being treated in the private King Edward VII Hospital in Marylebone, central London.
The prince remains "in good spirits," they added, while details of his illness are not being made public.
The palace said on Wednesday that Prince Philip was admitted as a "precautionary measure" on the advice of his doctor.
The prince was able to walk into the hospital unaided after arriving in private transport rather than an ambulance, a source said at the time.
He was not thought to have contracted coronavirus. Both he and Queen Elizabeth II received first doses of a Covid-19 vaccine in January.
Police officers continued to stand outside the doors of the hospital on Friday.
The latest update on Philip's health came as Buckingham Palace made a major announcement Friday regarding Prince Harry and his wife Meghan.
The palace said the couple would not return as working members of the royal family, after they stepped back from frontline duties last year and subsequently settled in California.