Sunak deepened a diplomatic row with Athens on Wednesday by accusing Mitsotakis of "grandstanding" during a recent trip to London over ownership of the Parthenon Sculptures.
Sunak cancelled a planned meeting with Mitsotakis earlier in the week.
A Buckingham Palace source said on Friday that Charles also wore the same tie last week, before the escalation of the dispute.
British media noted that, as well as the blue and white tie featuring the same white cross design as the Greek flag, Charles sported a blue and white handkerchief protruding from his jacket pocket.
The museum has said it would consider a loan to Greece only if Athens acknowledges the museum's ownership of the sculptures.
Persons:
Britain's King Charles, Rishi Sunak, Kyriakos, Charles, Sunak, Prince Philip, Mitsotakis, … King Charles, Chris Ship, Lord Elgin, Alistair Smout, Michael Holden, William Schomberg, Alex Richardson
Organizations:
United Arab Emirates, Greek, ITV television's, British Museum, Thomson
Locations:
DUBAI, COP28, Corfu, Sunak, Athens, London, Buckingham, Dubai, Greece, LONDON