Dr George Carey, who is on an eight-day visit to the Middle East, became the first Archbishop of Canterbury to address the 15,000 worshippers before Friday prayers at Abu Nour Mosque, the largest mosque in Damascus.
He began with the words: "Salaam aleikum! Peace be with you all!" before going on to say: "Sadly, when we look at the history of the world all too often we find it littered with the remains of conflicts between Christians and Muslims. This has led to a culture of distrust and to the tendency for each of us to demonise the other."
Such "demonising" ignored the great contribution both faiths can make to the world, he added. "The influence of our faiths, the strength of our worship, the enduring force of our traditions and the commitment to family life and the lives of our communities gives us a duty and a remakable opportunity to make a significant contribution to the human family and its future," he said.
Dr Carey warned against "aggressive proselytism". Both Christianity and Islam were missionary religions, a fact that could not be disguised nor denied, he said.
"But, despite all the inherent risks in this recognition, there is no reason why it should lead us towards conflict. Rather, it should instil in us a sense of respect, a respect for such enthusiasm and devotion of faith," Dr Carey said.
He hoped his presence at the mosque before Friday prayers "will be seen by Muslims everywhere as my commitment to a dialogue based on friendship, integrity and honesty - and above all respect between the members of both our faiths".