Christian doctrine is offensive to Muslims, the Archbishop of Canterbury said yesterday. Dr Rowan Williams also criticised Christianity's history for its violence, its use of harsh punishments and its betrayal of its peaceful principles.

His comments came in a highly conciliatory letter to Islamic leaders calling for an alliance between the two faiths for 'the common good'. But it risked fresh controversy for the Archbishop in the wake of his pronouncement earlier this year that a place should be found for Islamic sharia law in the British legal system.

In it, Dr Williams said violence is incompatible with the beliefs of either faith and that, once that principle is accepted, both can work together against poverty and prejudice and to help the environment.

He also said the Christian belief in the Trinity - that God is Father, Son and Holy Ghost at the same time - 'is difficult, sometimes offensive, to Muslims'. Trinitarian doctrine conflicts with the Islamic view that there is just one all-powerful God. Dr Williams added: 'It is all the more important for the sake of open and careful dialogue that we try to clarify what we do and do not mean by it, and so I trust that what follows will be read in this spirit.'

The Archbishop said that faiths which reject the use of violence should learn to defend each other in their mutual interest. 'If we are in the habit of defending each other, we ought to be able to learn to defend other groups and communities as well,' he said.

But his letter in reply to last year's Islamic approach, A Common Word for the Common Good, chimes with his view expressed in February that people of faith should be able to work together against secularism despite their differences. Officials pointed to the Archbishop's call for 'religious plurality' to turn to serving the common good and added: 'This is true even where truth claims may seem irreconcilable'.