In an outspoken attack, Dr Rowan Williams warned that the Government's policies in areas such as health and education were sparking "bafflement and indignation" among voters who had not seen them exposed to public debate in last year's election.
There was "anger and anxiety" at ministers' efforts to push through far-reaching reforms for which they had no democratic mandate, said the head of the Church of England.
The Prime Minister said Dr Williams was free to express his views, but he "profoundly disagreed" with many of his comments.
And some Tory backbenchers were indignant at the Archbishop's decision to intervene in the political debate, with one MP branding it "unacceptable".
Writing in the New Statesman, Dr Williams said: "With remarkable speed, we are being committed to radical, long-term policies for which no-one voted.
"At the very least, there is an understandable anxiety about what democracy means in such a context.
"The anxiety and anger have to do with the feeling that not enough has been exposed to proper public argument."
On welfare reform, he said there had been a resurgence of the language of "'deserving' and 'undeserving' poor", combined with a "steady pressure to increase what look like punitive responses to alleged abuses of the system".
And he was dismissive of Mr Cameron's "painfully stale" Big Society initiative to encourage community spirit, noting widespread suspicion that it was being pursued "for opportunistic or money-saving reasons".
Dr Williams added: "Government badly needs to hear just how much plain fear there is around questions such as these at present.
"It isn't enough to respond with what sounds like a mixture of 'This is the last government's legacy' and 'We'd like to do more, but just wait until the economy recovers a bit'."
Mr Cameron hit back by insisting the Government was acting in a "good and moral" fashion.
Speaking during a visit to Northern Ireland, he said: "I am absolutely convinced that our policies are about actually giving people a greater responsibility and greater chances in their life, and I will defend those very vigorously.
"By all means let us have a robust debate but I can tell you, it will always be a two-sided debate."
The Big Society was "an enormous opportunity, not just for the Church of England but for all religious organisations and faith groups to try and make sure they do even more of the wonderful work they do to improve the condition of people in our society", said Mr Cameron.
Work and Pensions Secretary Iain Duncan Smith denied resurrecting the Victorian concept of the "deserving poor" and said the Archbishop's criticisms of welfare policy were "a little unbalanced and unfair".
And Business Secretary Vince Cable said it was "a little odd" for him to suggest that the coalition's policies were being foisted on voters without sufficient scrutiny, as there was a "vigorous debate" over issues such as health reform.
But Tory backbenchers were less restrained in their reaction to the Archbishop's intervention.
North Thanet MP Roger Gale said: "For him, as an unelected member of the upper house and as an appointed and unelected primate, to criticise the coalition Government as undemocratic and not elected to carry through its programme is unacceptable."
And Gary Streeter, MP for South West Devon, said: "I think the people are with us on this and the Archbishop, sadly and unusually for him, has ill-judged his attack.
"I would just guess that most people would be slightly baffled by the Archbishop's comments."
Labour insisted many members of the public felt the same way as the Archbishop.
Frontbench spokesman Andy Burnham said: "Across the country, people who are seeing this Tory-led Government pursuing divisive policies without a mandate will share the Archbishop's concerns."
But there was a side-swipe at Labour in Dr Williams' article, which said the opposition needed to "define some achievable alternatives" to the Government's programme.
Labour's former prime minister Tony Blair - who appointed Dr Williams to Lambeth Palace in 2003 - said governments had to expect criticism from archbishops.
"Obviously people used to criticise our policies, not just on Iraq and foreign policy, but on domestic policy and reform as well. It's just part of the way things work," he said.
There was support for Dr Williams from within the Church. The Bishop of Guildford, the Rt Rev Christopher Hill, said his comments were "eminently reasonable".
"Government cannot at any stage simply abrogate its responsibility. One of the prime, core functions of government is the care of all in society, especially those at the bottom," he told the BBC.
"That is extremely important and a matter of deep concern."
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