Controversial: Dr Rowan Williams believes the introduction of Sharia law to Britain will help maintain social cohesion
Rowan Williams told BBC Radio 4's World At One that the UK has to "face up to the fact" that some of its citizens do not relate to the British legal system.
He says that Muslims could choose to have marital disputes or financial matters dealt with in a Sharia court. He added Muslims should not have to choose between "the stark alternatives of cultural loyalty or state loyalty".
Dr Williams said there was a place for finding a "constructive accommodation" in areas such as marriage - allowing Muslim women to avoid Western divorce proceedings.
Other religions enjoyed such tolerance of their own laws, he pointed out, but stressed that it could never be allowed to take precedence over an individual's rights as a citizen.
He said it would also require a change in perception of what Sharia involved beyond the "inhumanity" of extreme punishments and attitudes to women seen in some Islamic states.
Dr Williams said: "It seems unavoidable and, as a matter of fact, certain conditions of Sharia are already recognised in our society and under our law, so it is not as if we are bringing in an alien and rival system.
"We already have in this country a number of situations in which the internal law of religious communities is recognised by the law of the land as justifying conscientious objections in certain circumstances."
He added: "There is a place for finding what would be a constructive accommodation with some aspects of Muslim law as we already do with aspects of other kinds of religious law.
"It would be quite wrong to say that we could ever license a system of law for some community which gave people no right of appeal, no way of exercising the rights that are guaranteed to them as citizens in general.
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Sharia law in Britain would provide Muslims with an alternative to our divorce courts
"But there are ways of looking at marital disputes, for example, which provide an alternative to the divorce courts as we understand them.
"In some cultural and religious settings, they would seem more appropriate."
But his views were condemned today by senior Tory MP Peter Luff, who said: "This is a very dangerous route which we should not go down. You can't be a little bit pregnant. You can't have a little bit of sharia law.
"We should not start introducing new different legal systems alongside ours."
But the Archbishop defended his position saying people people needed to look at Islamic law "with a clear eye."
"They should not imagine, either, that we know exactly what we mean by Sharia and just associate it with ... Saudi Arabia, or whatever," he continued.
"Nobody in their right mind would want to see in this country the kind of inhumanity that has sometimes been associated with the practice of the law in some Islamic states: the extreme punishments, the attitudes to women."
There were questions about how it interacted with human rights, he said.
"But I do not think we should instantly spring to the conclusion that the whole of that world of jurisprudence and practice is somehow monstrously incompatible with human rights just because it doesn't immediately fit with how we understand it."
Dr Williams said Orthodox Jewish courts already operated in the UK, and anti-abortion views of Catholics and other Christians were "accommodated within the law".
"The whole idea that there are perfectly proper ways the law of the land pays respect to custom and community, that's already there."
He said the issue of whether Catholic adoption agencies would be forced under equality laws to accept gay parents showed there was confusion on the matter.
"That principle that there is only one law for everybody is an important pillar of our social identity as a Western democracy.
"But I think it is a misunderstanding to suppose that means people don't have other affiliations, other loyalties which shape and dictate how they behave in society and that the law needs to take some account of that."
He said he accepted people might be surprised by his call but urged them to consider the wider question.
"What we don't want is a stand-off where the law squares up to people's religious consciences, on something like abortion or indeed by forcing a vote on some aspects of the Human Fertilisation and Embryology Bill in the Commons ... we don't either want a situation where, because there's no legal way of monitoring what communities do, making them part of the public process, people do what they like in private in such a way that that becomes another way of intensifying oppression within a community."
Sharia law was originally more enlightened in its attitude to women than other legal systems, he pointed out, but did now have to be brought up to date.
"But you have to translate that into a setting where that whole area of the rights and liberties of women has moved on.
"The principle and the vision which animates the whole Islamic legal provision needs broadening because of that."
Responding to comments by one of his senior bishops that Islamic extremism was creating communities with "no-go areas" for non-Muslims, he said it was "not at all the case that we have absolute social exclusion.
"But we do have a lot of social suspicion, a lot of distance and we just have to go on working at how that shared citizenship comes through."
The Bishop of Rochester, The Rt Rev Dr Michael Nazir-Ali, said last month that non-Muslims faced a hostile reception in places dominated by the ideology of Islamic radicals.
Dr Williams said the use of the phrase "no-go areas" had sparked controversy because it reminded people of Northern Ireland.
"I don't think that was at all what was intended; I think it was meant to point to the silo problem, the sense of communities not communicating with each other.
"Many Muslims would say that they feel bits of British society are no-go areas for them."
Mohammed Shafiq, director of the Ramadhan Foundation, welcomed the comments.
"These comments further underline the attempts by both our great faiths to build respect and tolerance.
"Sharia law for civil matters is something which has been introduced in some Western countries with much success; I believe that Muslims would take huge comfort from the Government allowing civil matters being resolved according to their faith.
"We are however disappointed that the Archbishop of Canterbury was silent when Mr Nazir-Ali was promoting intolerance and lying about no-go areas for Christians in the UK by Muslim extremists.
"Unless he speaks out against this intolerance, Muslims will take his silence as authorisation and support for such comments.
"The Ramadhan Foundation will continue to work with the Church of England to build understanding and respect for our two communities."
Dr Williams's comments are likely to fuel the debate over multiculturalism in the UK.
But he insists that Sharia law needs to be better understood.
At the moment, he says "sensational reporting of opinion polls" clouds the issue.
