Archbishop Carey spoke at an Islamic study institute
Dr Carey used the main speech of his visit to the Gulf country of Bahrain to call on Muslims to ensure freedom of worship for Christian minorities.
But he said Christians in nations such as Indonesia, Pakistan, Nigeria and Sudan were not able to practise their faith with the same freedom that people of other faiths enjoyed in the west.
These Christians were perhaps in their most vulnerable position ever, he added.
"They need their Muslim brothers and sisters to speak up for them and, when extremists threaten, they need support and friendship," he said.
Necessary force
Earlier, the Archbishop of Canterbury said he believes the use of military force in Afghanistan is necessary to counter "a fanatical enemy".
In a BBC interview in Bahrain, Doctor George Carey said he saw no alternative to military action, although the violence used should be proportionate to the task.
He said the coalition of countries trying to capture Osama bin Laden was up against what he described as an evil enemy, intent on a path of destruction.
But Dr Carey stressed the conflict was not with Islam, and said Muslims and Christians must find a way to live in harmony together or face a bleak future.
'No alternative'
He said: "We're against an enemy who has no moral limits on what he will do to achieve his goals.
"Now when you ally that 'no moral limits' to a fanatical belief in God, then you have a very dangerous concoction. I don't think they had any alternative but to attack."
On his first visit to a Muslim country since the start of military action in Afghanistan, Dr Carey said it was wrong to equate Islam with some of the policies seen recently in Afghanistan, including the repression of women, but that faith all too often "gets mixed up with other ideological and political influences".
'Joining together'
Tension between the two faiths has risen following the massacre of 16 Christians in a church in the town of Bahawalpur in Pakistan last Sunday.
Dr Carey has described the massacre as a scar on relations between Christianity and Islam, appealing to Christians not to retaliate.
On Saturday he spoke of how one of the people killed in the massacre at Bahawalpur was a Muslim guard who lost his life trying to protect people whose
faith he did not share.
He said: "The newspapers in Britain this week were full of reports of how Muslims and Christians were in sorrow, side by side, mourning this great tragedy.
"How great it will be when, one day, Christians and Muslims will join together in laughter and celebration - and indeed pride - at the distance we have been able to travel together."
Dr Carey's visit was arranged before the terrorist attacks on America.
The 65-year-old archbishop served with the British armed forces in Iraq in the 1950s, and has said he still feels "sentimental links" with the region.
After his stay in Bahrain, Dr Carey will visit Qatar before returning to London.