The Most Rev Justin Welby suggested “some will have to come down” but said it is not his decision and that monuments would be put “in context”.
The Archbishop was asked if people should forgive the “trespasses” of people immortalised in the form of statues, rather than tearing them down.
He told BBC Radio 4’s Today programme: “We can only do that if we’ve got justice, which means the statue needs to be put in context. Some will have to come down.
“Some names will have to change.
“I mean, the church, goodness me, you know, you just go around Canterbury Cathedral, there’s monuments everywhere, or Westminster Abbey, and we’re looking at all that, and some will have to come down.
“But yes, there can be forgiveness, I hope and pray as we come together, but only if there’s justice.
“If we change the way we behave now, and say this was then and we learned from that, and change how we’re going to be in the future, internationally, as well.”
Pressed on whether he was saying statues will be taken down in the cathedral, Mr Welby said: “No, I didn’t say that. I very carefully didn’t say that.”
He said it is not his decision, and told the programme: “We’re going to be looking very carefully and putting them in context and seeing if they all should be there.”
Mr Welby added: “The question arises. Of course it does.”
He said it is “what people do at times like this”, adding: “And it’s a good thing, but there has to be, for forgiveness, there has to be this turning round, this conversion, the Pope called it.
“The change of heart that says we learned from them not to be like that, and to change the way we are in the future.”
With the growing surge in support for the Black Lives Matter movement, which has sparked global protests following the death of George Floyd at the hands of Minneapolis police, a number of petitions have emerged demanding controversial monuments in the UK are taken down.
In Bristol, a statue of slave trader Edward Colston was pulled down and dumped in the harbour, while the figure of slave owner Robert Milligan was taken down from its plinth at West India Quay in London’s Docklands.
Last week, the governing body of Oxford’s Oriel College “expressed their wish” to remove a statue of British imperialist Cecil Rhodes, following fresh protests.