The King began his Caribbean tour by acknowledging the “great suffering of the past” and confirmed that Commonwealth leaders will discuss the legacy of slavery at a major summit.

Speaking at an event celebrating Bahamas youth and staged where the country’s independence from the UK was declared, he said its culture was “born out of darkness”.

His visit comes in the wake of renewed calls from Caribbean nations for Britain to apologise for its role in selling enslaved people for profit and for reparations.

The nine-day regional tour, which includes a solo state visit to Guyana, will culminate in the Commonwealth Heads of Government Meeting (CHOGM) hosted by Antigua and Barbuda and presided over by the King, joined by the Queen, in his role as head of the “family of Nations”.

Charles told hundreds of schoolchildren and leading politicians: “Some of what is best in Bahamian culture today, the most joyful, the most hopeful, the most bright was born out of darkness.

“It is only right that we should acknowledge the great suffering and injustices of the past in these islands and beyond, even as we rejoice in the successes of the present and build new opportunities for the future.

“I know leaders of the governments of affected Commonwealth countries will be discussing these matters in Antigua and Barbuda next week.”

The King, then as Prince of Wales, attended the independence celebrations to deliver a formal message from Queen Elizabeth II to Bahamians.

He added: “This evening, though, it gives me enormous hope to see the way generations of Bahamians have carried the history, the legacy and the promise bequeathed to you by your ancestors, with pride in your hearts and purpose in your steps.

“Indeed, you have not only carried their legacy, you have nurtured and enhanced it, creatively and courageously, and we have seen tonight what a wonderful gift it is, to the Bahamas and to the world.”

Outside the grounds of the event was a small reparations protest of around a dozen people carrying placards with the words: “Pay us what you owe us”.

In the run-up to the leaders’ summit, the Commonwealth’s secretary general Shirley Botchwey said last week it “wouldn’t hurt” when asked during an interview whether the King should apologise.

And Guyana’s president, Mohamed Irfaan Ali, said recently that Charles has recognised slavery as the darkest days in human history – but moving to the apology is “the next step”.

The Prime Minister Andy Burnham and Foreign Secretary Ed Miliband will join the King in Antigua for the gathering of Commonwealth leaders.

The UK Government’s position on reparations is well established, it acknowledges the trade in enslaved people was abhorrent and its impact is still felt today, but it will not pay financial reparations for historical acts that did not break international laws at the time and is committed to continued dialogue with Commonwealth nations.

A Buckingham Palace spokesperson said: “At the request of host Governments, the King’s programme will primarily focus on shining a light on the many modern partnerships and opportunities for the future that are having a transformative effect on the region, as it confronts the challenges of today.

“For His Majesty, this tour is both a new journey but also the continuance of a lifelong one, in which he has sought to engage, understand and educate about the most shameful aspects of our past.

“This will therefore also be reflected in differing ways and words during the tour, as you would expect.”