CNN reported the group released a message saying, "The Ministry of War of Islamic State of Iraq declares that all the centers, organizations and bodies of Christian leaders and followers have become legitimate targets for the mujahedeen (holy warriors), wherever our hands will reach them."
On Monday, the group gave the Coptic church of Egypt 48 hours to reveal the status of Muslim women it asserts are being held captive in its churches.
The Islamic State of Iraq has claimed responsibility for Sunday's assault on a Baghdad church that killed 58 people and wounded 75. It includes several Sunni extremist groups and has ties to al-Qaida in Iraq.
The group cited the Egyptian women's alleged plight in storming the church.
Egyptian police sources confirmed that security has been reinforced at churches around the country and for the head of the Coptic Church, Pope Shenouda III.
The claim that the Copts are holding female captives is based on rumors of Christian women in Egypt converting to Islam and being held by the church to compel or persuade them to revert to their original faith.