Dr Rowan Williams sent a letter to Islamic leaders this week in which he called for an alliance between the two faiths “for the common good”.
He admitted that the belief in the Trinity is “difficult, sometimes offensive, to Muslims”.
But thHe also claimed that the existence of a variety of religions can be good for communities.
It comes after Dr Williams caused controversy by suggesting that there could be a place for Sharia law within the English legal system.
The archbishop wrote: “And here we can together suggest a way in which religious plurality can be seen as serving the cause of social unity and acting as a force for the common good.
“In a plural society, Christians secure their religious liberty by advocacy for the liberty of people of other faiths to have the same right to be heard.”
But some critics claimed the Archbishop of Canterbury, as the head of the Church of England and worldwide Anglican Communion, should be more of an advocate for his own faith rather than talking about the benefits of living in a multi-faith society.
The Rev David Phillips, general secretary of the conservative evangelical group The Church Society, said: “It’s a strange thing to say in a way, because it’s not really the end game for Christians, or for Muslims.
“It must be the role of the Archbishop of Canterbury to evangelise to other faiths.
“St Augustine, the first Archbishop of Canterbury, was a missionary from Rome. Just imagine what would have happened if he’d said we’re going to go to pagan England but we’re not going to convert people to Christianity.
“The danger is that someone in his role becomes over-cautious.”
Alison Ruoff, a prominent member of the Church of England’s governing body, the General Synod, said much of his letter was “helpful” but added: “As the archbishop says, we must continue the dialogue for peace and respect between Christians and Muslims.
“But what he doesn’t say is the Bible clearly states that Jesus says,’”I am the Way the Truth and the Life and no one comes to the Father, except through Me.’”
Yesterday hundreds of Anglican bishops from around the world arrived in Canterbury for the start of the Lambeth Conference, their once-a-decade gathering.
Dr Williams, who is trying to keep the church together despite deep divisions between liberals and conservatives over homosexuality and women bishops, will address them at a service at Canterbury Cathedral on Sunday.
In a welcome message for bishops arriving in Canterbury, Dr Williams acknowledged the tensions within the church.
He said: “Our Communion is living through very difficult times and we are bound to be aware of the divisions and conflicts that haveghra hurt us all in recent years.
“But, as the Lord says, it is in union with him that we shall find peace.” e archbishop claimed Christianity and Islam can work together for a “radical, transforming, non-violent engagement” and welcomed an open letter written by Muslim religious leaders and scholars about greater understanding between the faiths.