The Archbishop of Canterbury has defended his comments on Sharia law, following widespread criticism.
Dr Williams is said to be shocked by the response to his comments
A statement on his website said that he "certainly did not call for its introduction as some kind of parallel jurisdiction to the civil law".
However, at least two General Synod members have called for Dr Rowan Williams to resign following the row.
Col Edward Armitstead told the Daily Telegraph: "I don't think he is the man for the job."
Dr Williams had called for parts of Sharia law to be recognised in the UK, and he is said to be in a state of shock and dismayed by the criticism he has received from his own Church.
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.
Col Armitstead, a Synod member from the diocese of Bath and Wells, said Dr Williams should move to work in a university setting instead of leading the Anglican Church.
"One wants to be charitable, but I sense that he would be far happier in a university where he can kick around these sorts of ideas."
Alison Ruoff, a Synod member from London, said: "Many people, huge numbers of people, would be greatly relieved [if he resigned] because he sits on the fence over all sorts of things and we need strong, Christian, biblical leadership right now, as opposed to somebody who huffs and puffs around and vacillates from one thing to another.
"He's a very able, a brilliant scholar as a man but in terms of being a leader of the Christian community I think he's actually at the moment a disaster."
Brig William Dobbie, a former Synod member, described the archbishop as "a disaster, a tragic mistake".
The statement on the archbishop's website also said Dr Williams had pointed out that "as a matter of fact, certain provisions of Sharia are already recognised in our society and under our law".
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 said he was "exploring ways in which reasonable accommodation might be made within existing arrangements for religious conscience".
It also said his principal aim was "to tease out some of the broader issues around the rights of religious groups within a secular state".
And he said he did not initiate the idea but simply agreed when that proposition was put to him.
Dr Williams made his first public appearance since the controversy erupted at a thanksgiving service on Saturday, but he made no comment on the row.
The service, at Great St Mary's in Cambridge, was held to give thanks for the life of the Rev Professor Charles Moule, a New Testament scholar who died last year.
The archbishop has been defended by the most senior woman priest in the Church of England, the Dean of Salisbury the Very Reverend June Osborne, who said he was right to discuss Sharia law.
"We can say he may have been politically na´ve [but] I don't think he was.
"Our society needs to be provoked into talking about these things. I would say that all of the law of Britain has got to work within the very high standards of human rights and Christian principles."
The Muslim Council of Britain (MCB) said it was grateful for the Archbishop's "thoughtful intervention" on the discussion of the place of Islam and Muslims in modern Britain.
A spokesman said: "The MCB observes, with some sadness, the hysterical misrepresentations of his speech which serves only to drive a wedge between British people."
The Bishop of Hulme, the Rt Rev Stephen Lowe, said he was dismayed at the "knee-jerk" reaction to Dr Williams' comments.
"We have probably one of the greatest and the brightest Archbishops of Canterbury we have had for many a long day," he told BBC Radio 4.
"He is undoubtedly one of the finest minds of this nation.
"The way he has been ridiculed, lampooned and treated by some people and indeed some of the media within this process, is quite disgraceful."
Synod members will have the opportunity of tabling a motion to discuss the issue at the body's biannual meeting, starting on Monday.
It is more likely that Dr Williams will receive warm support, such is the respect and affection for him among Anglicans, BBC News religious affairs correspondent Robert Pigott said.
Dr Williams evidently wanted to provoke discussion about Sharia, but not the impassioned and confused debate that has taken place, our correspondent added.