Sisi identified the bomber as Mahmoud Shafik Mohamed Mostafa who blew himself up using an explosive belt yesterday.
The President, who who attending the official funeral of the victims in Cairo, said four persons, including a woman, have been arrested in connection with the deadliest attack against the minority community in recent times.
Two more suspects are being pursued, he added.
Early today, Sisi held a meeting with Prime Minister Sherif Ismail and a number of other senior officials to follow up on the investigations of the attack and the security measures around the country, a presidential statement said.
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The attack killed 25 people, mostly women and children, and wounded 49 others.
The explosive device containing about 12 kg of TNT exploded on the women's side of the cathedral, officials said.
A three-day mourning was declared in memory of those killed in the blast.
There was no immediate claim of responsibility for the attack, though Jihadists in Sinai often target Christians as well as Muslims they accuse of working with the government.
The head of Al-Azhar, Egypt's top Sunni authority, had also condemned the blast as "a great crime" against Egyptians.
Copts, who make up about 10 per cent of Egypt's population of 90 million, have faced persecution and discrimination that increased during the 30-year rule of Hosni Mubarak, who was toppled by a popular uprising in 2011.
Islamist extremists have regularly incited violence against the minority community, especially since the country's first Islamist President Mohamed Morsi was ousted by the military in 2013.
In 2011, a suicide bomber killed 21 worshippers outside a church in the coastal city of Alexandria.