Does Prince William withdraw his support for Prince Charles as head of the Commonwealth?
Jamaican Prime Minister Andrew Holness told William in front of television cameras that the nation was "continuing" as an independent country.
"I know this tour has brought up even sharper questions about the past and the future," the Duke of Cambridge said in a statement at the end of the tour on Saturday.
"In Belize, Jamaica and the Bahamas, that future is up to the people to decide."
William added that he and his wife "are committed to service" and that means "not telling people what to do" but "serving and supporting them."
Barbados formally declared itself a republic in November.
Belize, Jamaica and the Bahamas, all stops on the royal tour, are said to be considering such a move.
The Commonwealth, a grouping of 54 mostly former British colonies, is headed by Queen Elizabeth II.
In 2018, its leaders formally announced that her son and heir, Prince Charles, would inherit the position when he became king.
But William, second in line to the throne, said "I don't have in mind who the Commonwealth chooses to lead his family in the future."
“What matters to us is the potential of the Commonwealth family to create a better future for the people in it and our commitment to serve and support in the best possible way,” he added.
The Duke of Cambridge's comments have sparked a debate on social media, with some wondering if he has withdrawn his support for his father becoming the next head of the Commonwealth.