The Duke of Sussex says he immediately arranged to go to the UK after his father called to tell him he had cancer.
The palace said on Monday that the monarch had begun treatment for cancer, days after undergoing surgery.
The Prince of Wales also addressed Kate Middleton's recent surgery and hospital stay.
The monarch is currently still carrying out his constitutional duties after his cancer diagnosis.
A previous announcement of the monarch's enlarged prostate led to a significant increase in searches for the condition on the NHS website.
The Duke of Sussex quit royal duties in 2020 and moved to California.
The monarch received his diagnosis after his recent prostate surgery.
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The Princess of Wales, 42, is expected to remain hospitalised for the next 10 to 14 days following the planned procedure, Kensington Palace said.