Actor Sir Idris Elba offered words of sympathy to the King, remarking "sorry about the prime minister" after the Antiguan premier repeated calls for his country to become a republic.
Charles spoke briefly with the Luther actor when they met by chance at a popular historic tourist spot in Antigua while attending separate events.
The King is visiting Antigua to deliver the keynote address opening the Commonwealth Heads of Government Meeting (Chogm) on Tuesday, which is expected to be dominated by the issue of a slavery apology and reparations.
Antigua’s prime minister Gaston Browne reiterated on Sunday his personal ambition to replace the monarchy with an Antiguan head of state.
Speaking to ITV News, Mr Gaston said: "I can say to you, I am a Republican.
"So if you asked me about my personal view, I would like to see Antigua and Barbuda become a republic … but I have to recognise and accept the fact that there are certain constitutional provisions to become a republic, and that, ultimately, it is the decision of the people to determine whether or not we become a republic."
Charles was visiting Nelson’s Dock and had just placed an engraved stone into a wall when he met Sir Idris, a goodwill ambassador for the King’s Trust who was hosting the One Commonwealth Night concert at the Unesco World Heritage Site.
"How are you?" said the actor and knife crime campaigner as he shook hands with Charles, greeting him like an old friend.
The King asked "What are you doing here?" and, with both men laughing, Sir Idris replied "I get around", affectionately patting the King on the arm.
Elba added: "How are you doing though, are you having a good time? Sorry about the prime minister."
It is understood the actor was referring to Mr Browne.
Sir Idris, who first gained fame in the acclaimed US series The Wire, started acting after a grant from Charles’ Prince’s Trust helped him join the National Youth Music Theatre.
The 54-year-old celebrity, best known for playing DCI John Luther in the BBC crime series, was knighted earlier this year for services to young people.
The issue of a British apology for slavery and reparations is set to be central to discussions among world leaders at CHOGM whose countries experienced slavery.
Prime Minister Andy Burnham, in Antigua for the summit, said he is open to "listening to calls for a formal apology" from nations affected by the transatlantic slave trade, but ruled out financial reparations.
In his address, the King is expected to discuss slavery with "unflinching honesty" and "sincere sorrow".
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