Carey claimed that the next coronation needs "very significant changes" so that it is "inclusive" of other religions that have spread across Britain.
However, the current Archbishop of Canterbury, Dr Rowan Williams, disagrees. In a 2003 interview, Dr Williams emphasised the need for Prince Charles to stick to his duty to defend the Church of England when he becomes king. "Unless something really radical happens with the constitution, he is, like it or not, Defender of the Faith and he has a relationship with the Christian Church of a kind which he does not have with other faith communities."
The prince, who will become Supreme Governor of the Church of England when he becomes king, has already said that he wants to be Defender of Faith - not Defender of the Faith - when he accedes to the throne.
Lord Carey, 75, who remains an influential figure within the Anglican Church, made his comments in a television interview with Gyles Brandreth, the broadcaster and writer, for Channel 5.He said: "The Queen came to the throne at a time when the Church of England was really the only Christian faith in the country.
"And there were no Muslims, Sikhs, Hindus around to be in any way evident in the life of the country. Now it's a completely different world, so the coronation oath would have to be looked at more critically.
"It's got to be a much more interfaith coronation service next time around. Prince Charles put his finger on it and there's no way in which the sovereign can be defender of one faith. Although I hope that the next coronation will say very firmly that Christianity is still the dominant faith of the United Kingdom... it's got to be a much more inclusive character."
His comments follow a Home Office report, aimed at tackling "religious discrimination", which said that a coronation oath in which the monarch swears to uphold the Protestant faith may not be appropriate in modern, multi-faith Britain.
Although Lord Carey's comments are likely to be welcomed by Prince Charles, they are unlikely to be welcomed at Lambeth Palace.
