The Rt Rev David Jenkins said he believed elements of the story, including the three wise men, were 'mythical'. But Dr Carey said his remarks were not in keeping with the spirit of Christmas most people wanted.
A statement issued from Lambeth Palace said: 'The Archbishop regrets that the Bishop of Durham should have reopened these divisive issues in the run-up to Christmas, when most Christians would prefer to remember all that unites them in wonder at the Incarnation of our Lord.'
Liberty of thought and of interpretation of the detail of the Scriptures was part of the Anglican tradition.
The statement continues: 'He wishes to point out that the core of Dr Jenkins' theology has always been and remains the Incarnation of God in Jesus Christ.
'We celebrate Jesus' birth because it is in Jesus that we meet God in all His fullness. That is what we should be reflecting on and thanking God for this Christmas time.'
The Bishop, the fourth most senior man in the Church, said elements of the story fitted so well together 'that they look like compositions to express the faith that already existed'.
Asked on Sunday whether he believed in a star guiding the three kings to Bethlehem, Dr Jenkins said: 'On balance, I have to be frank and say no.'