Prince Philip's condition has "slightly improved", his daughter-in-law Camilla has said.
The Duke of Edinburgh has spent the past 15 days in hospital and was transferred to St Bartholomew's in central London on Monday.
He is undergoing treatment for a pre-existing heart condition and an infection, Buckingham Palace said.
The royal family is "keeping its fingers crossed" for Philip, Camilla, the Duchess of Cornwall, 73, said on Wednesday.
She said her father-in-law, 99, still "hurts at moments", when a volunteer at the vaccination centre in Croydon asked about his health.
Camilla is married to Prince Charles, the eldest son of Philip and Queen Elizabeth II.
The duke was first admitted to King Edward VII’s Hospital, also in London, on 16 February to receive treatment for an infection.
The hospital move to St Bartholomew's, a specialist cardiac care facility, heightened concerns for the duke, who will turn 100 in June.
He was to undergo further treatment alongside testing and observation for his pre-existing heart condition.
Buckingham Palace said on Monday that Philip was "comfortable and is responding to treatment but is expected to remain in hospital until at least the end of the week”.
The two-week stay is already Philip's longest-ever stint in hospital.
Philip, who retired from royal duties in 2017, rarely appears in public.
During the current coronavirus lockdown Philip had been staying at Windsor Castle with the Queen.
Additional reporting by agencies
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