Representatives of 56 countries, most with roots in Britain's empire, are attending the Commonwealth Heads of Government Meeting (CHOGM) that began in Samoa on Monday.
"I understand from listening to people across the Commonwealth how the most painful aspects of our past continue to resonate," King Charles said in a speech to the summit.
"It is vital, therefore, that we understand our history, to guide us towards making the right choices in future."
The demand for Britain to pay reparations or make other amends for transatlantic slavery is a long-standing one, but has recently gained momentum worldwide, particularly among the Caribbean Community (CARICOM) and the African Union.
Opponents of reparations payments say countries should not be held responsible for historical wrongs, while those in favour say the legacy of slavery has led to vast and persistent racial inequality today.
British Prime Minister Kier Starmer said on Monday the country would listen to nations who wanted to discuss the issue at the summit, but ruled out apologising for the country's historic role in the trade.
Bahamas Foreign Minister Frederick Mitchell told the BBC on Thursday the summit's draft conclusion, expected to be published on Saturday, had paragraphs calling for a discussion on reparations.
From the 15th to the 19th century, at least 12.5 million Africans were kidnapped and forcibly taken by European ships and merchants and sold into slavery.
Those who survived the brutal voyages ended up toiling on plantations in inhumane conditions in the Americas, while others profited from their labour.
"We have demonstrated an unparalleled ability to confound the painful history which brought us together and sit together as equals for 75 years," Commonwealth Secretary-General Baroness Patricia Scotland, a British diplomat and lawyer who was born in Dominica, told the summit.
