Prince Charles has told Commonwealth leaders he cannot describe "the depths of his personal sorrow" at the suffering caused by the slave trade.
Speaking in Rwanda, he said the potential of the family of nations could only be realised by acknowledging the wrongs that had "shaped our past".
Charles added it was up to states to decide if they remained monarchies or became republics in the future.
He also met the PM after reports he had criticised the UK's Rwanda asylum plan.
Some 54 countries are members of the Commonwealth, of which the Queen is the head.
The summit of leaders was postponed in 2020 and 2021 because of the pandemic and has not been held for four years.
Prince Charles - who is representing the Queen at the Commonwealth Heads of Government Meeting (Chogm) - described how he was on a personal journey of discovery and was continuing to "deepen my own understanding of slavery's enduring impact".
He said he was aware the roots of the Commonwealth organisation "run deep into the most painful period of our history" and said acknowledging the wrongs of the past was a "conversation whose time has come".
"I cannot describe the depths of my personal sorrow at the suffering of so many."
The Prince of Wales also told leaders their diversity was a strength they could use to "speak up for the values which bind us".
This was a significant speech by Prince Charles for two particular reasons.
He acknowledged a past wrong and a future aspiration.
The fact that he spoke about the slave trade in an African setting and to an audience which included many leaders from Africa and the Caribbean added to the resonance of his remarks.
It was, as he said, a "conversation whose time had come".
There was no apology as such for Britain's participation in the slave trade but there was an expression of personal sorrow.
Then on the constitutional debate within some of those Commonwealth countries which still have the British monarch as head of state he acknowledged that this was a decision - to remain as monarchies or become republics - which was entirely for them.
Even if they decided to transition to a new constitution (as Barbados did last November) this could be achieved with the Commonwealth framework without rancour.
All in all the impression was of a future British king and head of the Commonwealth keen to make his mark on two sensitive issues.
On Friday, the Commonwealth heads will discuss trade, health and the climate.
In his own speech at the opening, Boris Johnson spoke about the Covid pandemic and praised those behind the Oxford-AstraZeneca vaccine - 1.4 billion doses of which he said had been delivered to Commonwealth countries.
The pandemic posed a common threat to all humanity, Mr Johnson said, as does "catastrophic climate change".
"No-one understands this better than our Commonwealth friends in the Caribbean, the Pacific and the Indian Ocean, who can see the incoming tides surging ever higher up their beaches, threatening to inundate their villages and towns and in time the entire land mass of some island state."
He said the developed world had an obligation "to help our friends to cope with a danger they had no hand in causing".
Mr Johnson - who travelled to Rwanda with his wife Carrie Johnson - also spoke about the importance of education for women, saying: "If I could imagine a silver bullet that would solve an array of problems and transform countless lives, it would be to give every girl in the world the chance to go to school."
Earlier, Downing Street said it was "unlikely" the UK's Rwanda asylum policy would come up when the PM and prince met.
The policy would see the UK send some refugees, who have arrived in the UK through what the government has called "illegal, dangerous or unnecessary methods", to Rwanda to claim asylum there.
They may be granted permanent refugee status to stay in Rwanda. If not, they can apply to settle there on other grounds, or seek asylum in a "safe third country".
The first planned flight last week was cancelled minutes before take-off following a late legal challenge.
The heir to the throne is reported to have described the plan as "appalling", but a Clarence House spokesperson said the "prince is politically neutral".
Mr Johnson said he would not comment on anything the prince said to him.
Speaking to broadcasters hours before the meeting with Charles, he said: "I think people can see that a lot of prejudices about Rwanda need to be blown away.
"And actually the achievements of the government of Rwanda over the last couple of decades have been remarkable."
The prime minister said "people need to keep an open mind about the policy".
Before the summit, Prince Charles and the Duchess of Cornwall met Rwandan President Paul Kagame and First Lady Jeanette Kagame, Commonwealth Secretary General Baroness Scotland and Mr Johnson and his wife.
The three topics on the summit's agenda include sustainability, youth and the history and values of the Commonwealth.
Following the opening ceremony, leaders and representatives from most member countries will hold two days of talks behind closed doors.