The prime minister's statement comes a day after he was accused by the former archbishop of Canterbury Lord Carey of making Christians feel marginalised.
But writing in the Daily Mail, Lord Carey - who was Archbishop of Canterbury between 1991 and 2002 - said the bishops "cannot lay claim to the moral high-ground".
Former Archbishop of Canterbury, Lord Carey, has publicly backed the four Christians.
The previous Archbishop of Canterbury, Lord Williams of Oystermouth, left his post at the end of last year to become Master of Magdalene College, Cambridge.
The signatories include former Conservative leadership challenger David Davis, ex-ministers Tim Loughton, Sir Gerald Howarth and Sir Jim Paice, and the former Archbishop of Canterbury, Lord Carey of Clifton.
Mr Pitcher - who served for a brief and, he acknowledges, frustrating spell as public affairs secretary to the former Archbishop of Canterbury, Lord Williams, saves his most severe criticism for Lambeth Palace itself.
The Pope later met representatives of other faiths, including the Chief Rabbi Lord Sacks, and will go on to visit Archbishop of Canterbury Rowan Williams at Lambeth Palace.
Dr. Rowan Williams, the Archbishop of Canterbury, and Lord Phillips, the former Lord Chief Justice, argued in 2008 that Sharia courts should be used to resolve disputes among Muslims.
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Lord Williams, who had been the 104th Archbishop of Canterbury since 2002, stood down in December.
Over in the Lords (from 2.30pm), the first event of the day is the introduction of the former Archbishop of Canterbury, Rowan Williams, who is reincarnated back into the House as Lord Williams of Oystermouth.
Labour peer Lord Mitchell put down the amendment to the bill, which was also signed by Justin Welby, the incoming Archbishop of Canterbury.
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