Pressure has mounted on the Archbishop of Canterbury after his comments about Islamic Sharia law were criticised by his predecessor.
Lord Carey said his successor was a "great leader"
Lord Carey said Dr Rowan Williams's suggested acceptance of some Muslim laws was "a view I cannot share".
But, writing in the News of the World, he said Dr Williams should not be forced to quit.
Dr Williams has insisted he was not advocating a parallel set of laws, but has faced calls for his resignation.
Supporters have described the reaction to his comments as "hysterical".
Dr Williams sparked a major row after saying, in a BBC Radio 4 interview last week, that the adoption of parts of the law was "unavoidable" in Britain.
He is said to be shocked by the reaction and said on his website he "certainly did not call for its introduction as some kind of parallel jurisdiction to the civil law".
But the criticism continued as Lord Carey warned: "He has in my opinion overstated the case for accommodating Islamic legal codes.
Dr Williams is said to be shocked by the response to his comments
"His conclusion that Britain will eventually have to concede some place in law for aspects of Sharia is a view I cannot share.
"There can be no exceptions to the laws of our land which have been so painfully honed by the struggle for democracy and human rights.
"His acceptance of some Muslim laws within British law would be disastrous for the nation."
But he added: "He is a great leader in the Anglican tradition and he has a very important role to play in the Church."
'Classic British row'
Senior politicians defended the use of religious courts to arbitrate in disputes such as marital issues but said they could never challenge civil law.
Geoff Hoon, the government's chief whip, told Sky News Dr Williams should be able to stimulate debate but questioned the wisdom of him commenting on "complicated legal matters".
Tory former chancellor Ken Clarke said Dr Williams was an "unworldly man" who had got himself into "an absolutely classic British row".
"He has angered a lot of people because they have all been persuaded that he has been talking about bringing back the stoning of women for various moral offences and so on, which plainly he is just about the last person on earth to contemplate."
Further criticism came from Greg Venables, the Anglican Archbishop of the Southern Cone, which covers much of South America.
He expressed concern at the timing of the speech when there was tension between Christians and Muslims in some parts of the world.
He told the BBC: "Taken within the context of other things that have been said and done in recent months, it would just add to a general sense that confidence in the leadership of the Anglican church has plummeted."
BBC News religious affairs correspondent Robert Pigott said it was "pretty inconceivable" that Dr Williams would resign but warned the intervention by Archbishop Venables was a "severe swipe".
"A lot of the conservatives in the Anglican communion worldwide, and they make up tens of millions of people, clearly the majority, live cheek by jowl with Muslims and a lot of them have real issues with Sharia law," he added.
Dr Williams did not refer to the issue while preaching at a memorial service in Cambridge on Saturday, where he was briefly heckled on leaving.
He is thought likely to do so during his address to the General Synod in London on Monday.
Dr Williams was offered support by the Right Reverend George Cassidy, Bishop of Southwell and Nottingham, who branded the reaction "hysterical" and said the archbishop was simply trying to take forward a serious public debate.
He was also defended by the most senior woman priest in the Church of England, the Dean of Salisbury the Very Reverend June Osborne, who said: "Our society needs to be provoked into talking about these things."
And the Muslim Council of Britain welcomed his "thoughtful intervention" on the discussion of the place of Islam and Muslims in modern Britain.
But two General Synod members have urged him to quit.
Col Edward Armitstead, from the diocese of Bath and Wells, said he did not think Dr Williams was "the man for the job".
Alison Ruoff, from London, hailed him as a brilliant scholar, but added: "In terms of being a leader of the Christian community I think he's actually at the moment a disaster."
Sharia law is Islam's legal system
It is derived from the Koran and the life of the prophet Mohammed
Sharia rulings help Muslims understand how they should lead their lives
A formal legal ruling is called a fatwa
In the West, Sharia courts deal mainly with family and business issues
English law recognises religious courts as a means of arbitration
The statement on the archbishop's website said Dr Williams said certain provisions of Sharia were "already recognised in our society and under our law".
It added that he was exploring how "reasonable accommodation might be made within existing arrangements for religious conscience" and seeking "to tease out some of the broader issues around the rights of religious groups within a secular state".
Catholic leader Cardinal Cormac Murphy-O'Connor said he was "saddened" by the way the archbishop had been misunderstood.
"I think he did raise a point of considerable interest and concern at the moment, namely, the rights of a religious groups within secular state.
"Everyone in Britain must obey the law and therefore the question of how one can be a loyal British citizen and a faithful member of a religious group is a very pertinent question," he told BBC Radio 4's Sunday programme.