In a sermon in the southern Sudanese city of Juba on Sunday morning, Dr Carey called for misconceptions and misunderstandings to be put aside in the interests of peace and reconciliation.
"Some people in the West paint the conflict in Sudan as one between Christianity and Islam" he said. "Some in this country claim that Islam is the indigenous faith of Sudan and Christianity is a western import. Neither view is true.
"I do not believe there is any reason either here in Sudan or anywhere else in the world for Christians and Muslims to commit violence against one another. There is every reason to hold one another's faith in the deepest respect. And even more reason to discover common ground upon which together you can contribute to the peace process here. The suffering, the poverty the effects of war do not differentiate between religions. All the people of this beautiful country are suffering and all deserve peace."
Dr Carey, who is President of the world-wide Anglican Communion, was guest of honour at the enthronement in Juba of the new Anglican Archbishop of Sudan, the Most Reverend Joseph Marona. He described it as the opening of a new chapter in the history of the Church in Sudan.
The post had been vacant for two years-largely as a consequence of the devastating civil war, which is estimated to have cost over a million lives and left several million people homeless and destitute. Much of the area surrounding Juba is held by forces opposed to the pro-Islamic government and access to the city has been difficult.
Dr Carey, making his first visit to Sudan for five years- rejected discrimination against the country's Christian minority and appealed to the Churches to keep working together for an end to bloodshed and violence.
"The united witness of Christians in this country is of prime importance in the search for peace. I know how difficult life has been in many parts of the North-schools and churches destroyed, land confiscated and so on. I am glad to know that Christians of different traditions have turned out to support one another in their protests when these wrongs have been committed"
Dr Carey, who recently warned against 'Africa fatigue', said there were reasons for hope:
I know that for long periods of your recent history, you have felt abandoned, alone, unloved by the rest of the world. I do not think that has ever been the case. But I do understand how, when many have lived your daily lives in fear of violence oppression and arrest, the love and prayers of others can seem a great distance away.
"However, there has been a distinct growth of concern in the international community about the persistence of war in Sudan, and the lack of energy amongst those who are fighting, seriously, to search for peace. There are now many around the world who are determined to support the peace process".
Dr Carey flew to Juba from the Sudanese capital Khartoum, where he had talks on Saturday with government leaders, and preached at an ecumenical service in the Roman Catholic Cathedral.
He also toured a refugee camp for thousands of displaced families on the outskirts of the city and visited a school and a local church.