Bishop Angaelos said the northern African nation was becoming 'more vulnerable to a disturbing wave of radicalism' because of a downturn in tourism, economic problems and loss of foreign trade.
He warned of 'heightened, targeted attacks against Coptic Christians in Egypt' and said tensions between Christianity and Islam has 'escalated over the past few months'.
The violence will 'spiral even further if not immediately addressed', Bishop Angaelos said.
The public humiliation of a 70-year-old Christian woman shocked the world in May after her son was accused of having an affair with a Muslim woman.
"At their most brutal, these recent attacks have culminated in the burning of churches and places of worship, the stripping and public parading of 70-year-old Souad Thabet, and the senseless murder of Father Raphael Moussa," decried Bishop Angaelos.
The clergyman acknowledged there were 'clear efforts' by Egyptian officials to curb Christian persecution but said forces at a local level were guilty of 'at best, carelessness and, at worst, criminal negligence'.
He said the poor response from local police to attacks on Christians "gives a clear and direct message that certain crimes will go unchallenged and unchecked, especially when perpetrators are not brought to justice.
"The resulting sense of impunity not only means a lack of justice for crimes already perpetrated, but also gives greater encouragement to those who will seek to do even more, and more aggressively."
He added: "The brutal and personal nature of many of the attacks against our brothers and sisters in Egypt warrants our prayers and support for them as they continue to endure heightened levels of persecution while refusing to lose their admirable and resilient spirit, and unyielding ability to forgive according to their Christian devotion and commitment."