Prince William has publicly addressed the health of his grandfather Prince Philip.

William, 38, exchanged a few words on Monday with longstanding royals photographer Arthur Edwards, who asked him how Philip, 99, was doing.

"He's okay," said William. "They're keeping an eye on him."

Philip was admitted to King Edward VII Hospital in London on February 16 after "feeling unwell," the palace said.

William spoke with Edwards at a vaccine center in Norfolk, not far from his country home, Anmer Hall, where he and wife Kate Middleton and their children have been living during the latest U.K. lockdown.

Philip had been expected to remain in the hospital for a few days but on Friday, a royal source told PEOPLE that he would stay there into this week.

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"Following consultation with his doctor, the Duke of Edinburgh is likely to remain in hospital for observation and rest over the weekend and into next week," the source said. "The doctor is acting with an abundance of caution. The Duke remains in good spirits."

Palace sources stressed after Tuesday's admission to the hospital that this was not an emergency admission and that Philip walked into the hospital unaided. The illness is not COVID-19-related.

Philip had a visit from his eldest son Prince Charles, 72, on Saturday. Charles was photographed arriving at the hospital, via a rear entrance, wearing a gray suit and a face mask.

William's visit to the Norfolk vaccine center was his first official duty away from home this year. During the appearance, William — who contracted the coronavirus last April — met some of those being vaccinated and spoke to National Health Service staff and volunteers about their experiences of being a part of the largest vaccination program in British history.

He made the short journey from Anmer Hall, where he, Kate and their kids Prince George, Princess Charlotte and Prince Louis have been staying during the latest U.K.-wide lockdown due to the coronavirus pandemic.

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