In a message shared online after the blast at a chapel next to St Mark's Cathedral, it also vowed to "continue war against apostates".
The alleged attacker has been identified by Egyptian President el-Sissi as 22 year old Mahmoud Shafiq Mohammed Mustafa, who it claims belongs to a terror group funded by Muslim Brotherhood leaders.
The Muslim Brotherhood group, whose senior leaders include the ousted former-Egyptian president Mohammed Morsi, condemned the bombing.
CCTV footage released by the Egyptian government on Monday showed a figure crossing the street and walking through the gates of the church, before an explosion sends dust and debris into the air.
Christian activist, Nader Shokry, said: "How did all this planning take place without the security knowing about it?"
"You are saying that this person belongs to a terror group and has been previously arrested... So you should have kept a close eye on him."
The incident, which left 80 people injured, is among the deadliest attacks in recent memory against Egypt's Coptic minority which compromises of around ten per cent of the population.