The Archbishop of Canterbury is said to be overwhelmed by the "hostility of the response" after his call for parts of Sharia law to be recognised in the UK.
Dr Williams has been taken aback by the response to his comments
Friends of Dr Rowan Williams say he is in a state of shock and dismayed by the criticism from his own Church.
All the main political parties, secular groups and some senior Muslims have expressed dismay at his comments.
However, the Bishop of Hulme, the Rt Rev Stephen Lowe, criticised the "disgraceful" treatment of Dr Williams.
The BBC understands from sources who work on Christian-Muslim interfaith issues that Dr Williams has faced a barrage of criticism from within the Church and has been genuinely taken aback by how his words were received.
Islamic Sharia law is a legal and social code designed to help Muslims live their daily lives, but it has proved controversial in the West for the extreme nature of some of its punishments.
BBC News religious affairs correspondent Robert Pigott says both traditionalists and liberals in the Church have their own reasons for criticising Dr Williams.
Traditionalists maintain that English law is based on Biblical values and that no parallel system could be tolerated in the UK.
Liberal Anglicans believe giving Sharia legal status would be to the detriment of women and gay people.
Among those critical of the archbishop is the chairman of evangelical Church group Reform, the Reverend Rod Thomas.
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 Church at the moment, and the country, needs a clear lead. The country is itself in a debate about its own sense of identity," he said.
"The moral values that we pursue are ones that we need to know are clearly grounded, and it would be most helpful for the leader of the Church to be able to explain to people how the values we cherish stem from our Christian tradition."
UKIP MEP Gerard Batten said it would be the "thin end of the wedge" and called on the archbishop to resign.
He said: "I think he's shown he is totally unfit for the role he undertakes. He's not fit to be Archbishop of Canterbury, he doesn't seem to know what his own business is, and he's not fit to sit in the House of Lords. I think he should go."
However, there has been some support for Dr Williams.
The Muslim Council of Britain (MCB) said it was grateful for the archbishop's "thoughtful intervention".
The organisation added that it was saddened by the "hysterical misrepresentations" of his speech, which would only "drive a wedge between British people".
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Muhammed Abdul Bari, Secretary-General of the MCB, said: "The archbishop is not advocating implementation of the Islamic penal system in Britain.
"His recommendation is confined to the civil system of Sharia law, and only in accordance with English law and agreeable to established notions of human rights."
The archbishop had been "ridiculed" and "lampooned" by some people, according to Bishop Lowe.
"We have probably one of the greatest and the brightest Archbishops of Canterbury we have had for many a long day," he said.
Catherine Heseltine, from the Muslim Public Affairs Committee, said some people might be getting the wrong end of the stick.
"I'm concerned this debate is getting out of control because people hear the word Sharia and instantly scary images of beheadings," she said.
Dr Williams told BBC Radio 4 on Thursday that he believed the adoption of some Sharia law in the UK seemed "unavoidable".
In an interview with BBC correspondent Christopher Landau, Dr Williams said Muslims should not have to choose between "the stark alternatives of cultural loyalty or state loyalty".
Under English law, people may devise their own way to settle a dispute in front of an agreed third party as long as both sides agree to the process.
Muslim Sharia courts and Orthodox Jewish courts which already exist in the UK come into this category.