The IS statement said that a suicide bomber referred to as Abu Abdullah al-Masry carried out the attack with an explosive belt, killing and injuring 80.
"This blow has caused us a lot of pain, but never will we let it break us", Sisi said.
The bombing, which took place on Sunday, hit the church attached to one of Egypt's most symbolic sites for Copts, St. Mark's Coptic Cathedral.
The blast shattered windows and scattered pews through the interior of the church, scorching its marble pillars.
The Interior Ministry stated that "financial and logistical support" for the bombing was provided by leaders of the Brotherhood as it claims that Mahmoud joined a cell led by Mohab Mostafa Sayyed Qassem, a militant with links to IS fighters in Northern Sinai and exiled Brotherhood officials in Qatar.
Security sources said a bomb containing at least 26 pounds of TNT exploded on a side of the church normally used by women. The ministry said that Mostafa had been arrested in March 2014 for carrying arms during a protest and was freed on bail after two months, and that he was wanted in connection with two other cases. Bilal claimed to have spoken to her son in the past week and said he had not been radicalized, despite allegedly being beaten in custody.
She said his father had died two years ago, and that Mostafa called her regularly from overseas, most recently about a week ago.
Egyptian authorities accuse Doha of harboring members of Morsi's Muslim Brotherhood, which Cairo has designated as a "terrorist" organization.
"He said he would not return because security forces would detain him again". Mursi became president, but was toppled two years later after mass protests.
The perpetrator of the attack was "a martyrdom seeker of the Islamic State", the group's Aamaq Agency media outlet said last night. The Egyptian government had earlier released footage showing images said to be that of the alleged suicide attacker.
The group warned of more attacks to come. The army has responded with air strikes and by bulldozing entire villages.