The campaign group has accused Charles of hiding behind government advice in the face of calls for a slave trade apology.
Republic, which campaigns for the abolition of the monarchy, has insisted Charles owes a personal apology and should be making personal reparations from his own multi-billion-pound wealth.
Speaking while Charles visits the Caribbean, Republic's CEO Graham Smith said:
"Too often talk of Charles's lack of apology and the question of reparations is linked to government advice and the assumption Charles must only act on behalf of the UK."
"This ignores the fact Charles is sitting on a huge fortune that originates from the slave trade."
"The palace wants to ignore the long and grubby history of British monarchs supporting, sponsoring and profiting from the European trans-Atlantic slave trade."
"The huge fortune stolen from Africans - from Elizabeth I to William IV - has been inherited down the line of monarchs ever since."
"The royals justify their archaic position and privilege with calls back to our nation's long and chequered history."
"They cannot demand their privilege because of our history and in the same breath say that history has nothing to do with them."
"They cannot ignore calls for reparations when so much of their wealth was stolen from generations of Africans who were kidnapped, abused, murdered and enslaved by their own family's enterprises."
"The inter-generational poverty in the Caribbean and the inter-generational wealth of the royals are directly linked. Because the royals enslaved, abused and stole from generations of Africans and their Caribbean descendants."
"Let the British government decide what Britain will do - but Charles and William have their own apologies to make, and their own multi-million-pound reparations to surrender to the people of the Caribbean."
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