Andy Burnham has said he is "open" to calls for Britain to make a formal apology for its role in the slave trade as the King continues his tour of the Caribbean.
The prime minister is due to attend the Commonwealth Heads of Government Meeting (CHOGM) in Antigua and Barbuda - as is the King who, as the head of the "family of nations", will preside over the event.
Charles will give the opening address to national representatives of the 56 member states on Tuesday.
His speech is likely to echo the government's changed position on the legacy of slavery, the Press Association reports.
Ahead of his nine-day trip, it was understood ministers had not advised the King to offer an apology or reparations, in keeping with established policy.
But a formal apology is now potentially closer following comments made by Mr Burnham to the Guardian on Friday.
More from Sky News:
Is the 'manosphere' as dangerous as smoking?
Yorkshire Water boss resigns
The prime minister wrote: "We are offering a structured dialogue with those affected by the transatlantic slave trade.
"Listening to calls for a formal apology on behalf of the British state will form an important part of this process and I am open to them."
Mr Burnham expressed his "sorrow and regret for the pain and suffering of so many millions" but ruled out financial reparations.
He wrote: "Some have called for financial reparations for the slave trade. I do not believe that is the right answer.
"I do not think that British people today can be held liable for historical wrongs, however heinous, that happened in a different age under different laws and in which they played no personal part."
The Prime Minister of Barbados, Mia Mottley, said in a post on X: "Barbados welcomes the UK Prime Minister's acknowledgement of the brutality of the transatlantic slave trade, his openness to a formal apology and his offer of structured dialogue."
Jamaica's Prime Minister, Andrew Holness, said of Mr Burnham's comments: "Open minded dialogue is always a good place to start addressing difficult issues."
Caribbean nations again urged Britain to apologise for its role in selling enslaved people, and for reparations, in the lead-up to the King's Caribbean tour.
Before leaving Guyana on Friday, the King visited Independence Park in the capital, Georgetown, where 33 people involved in the Demerara Rebellion of 1823 were hanged.
He was joined by Guyana's culture minister Steven Jacobs to acknowledge the country's history of slavery and resistance.
Charles started his Caribbean trip last Tuesday with a speech at a youth rally in the Bahamas, where he commented on the "great suffering of the past".
Prior to the visit, Guyana's President Mohamed Irfaan Ali said the King had recognised slavery as the darkest moments in human history, but an apology would be "the next step".
(c) Sky News 2026: Burnham 'open' to slavery apology - as King continues Caribbean tour
Virgin Media O2 to axe thousands of jobs in sweeping shake-up
Police investigating Andrew's Balmoral stays with Epstein and Maxwell
Motorist who dragged cyclist under his car for more than a mile guilty of murder
G20 photocall cancelled after Ed Miliband and other foreign ministers refuse to be pictured with Russia's Sergei Lavrov
Man arrested as part of probe into suspected terrorism offences in Belfast
Three explosive devices found as police detain man and woman in Essex
Former non-league football club boss admits offences linked to rape of woman drugged by husband
Yorkshire Water boss resigns after company given lowest environmental rating
Watchdog investigating Met Police over handling of letter about Meghan's father
