Lord Carey said more had to be done to support followers of Christ who face persecution or death at the hands of Islamic terrorism.
"Time is running out for Christians in the region," he said.
Hundreds of thousands of Christians have been killed or forced to flee their homes as Islamic State advances over parts of Iraq and Syria.
Those that are not murdered are forced to convert to Islam or pay a tax for being Christian.
Speaking in the Sunday Express Lord Carey added: "They are now facing an existential threat to their very survival. Successive UK governments have failed to do enough to support minority communities in the Middle East and now sadly, many Christians have concluded they have no future in a region where they have lived for nearly two thousand years.
"I urge David Cameron, to consider the claims of Christian communities for asylum and to pursue both diplomatic and military means to end the threat of Islamist violence against minority communities."