The suicide bomber was 22-year-old Mahmoud Shafiq Mohamed Mostafa, who entered the church wearing an explosive belt, el-Sisi said. He added that authorities are searching for more suspects in the attack, which left 23 people dead and 49 others injured.
Meanwhile, mourners took to the streets to pay their respects to those who died in the bombing of the small church of St. Peter and St. Paul, which is attached to St. Mark's Coptic Orthodox Cathedral in the city's Abbassiya district.
Mood on the street
The funeral procession for the victims was held Monday at the Church of the Virgin Mary in Nasr City and was followed by a state funeral at the Unknown Soldier Memorial.
"This strike hurt us," el-Sisi said at the state funeral. "It caused us a lot of pain, but it will never break us."
Crowds lined the streets outside the church, with some trying to reach the ambulances carrying the coffins and the procession.
There were light skirmishes between mourners and security forces as police refused to let the crowds through to the funeral procession.
One woman cried at police, "You let people enter the church with a bomb but you won't let us in?"
People began to break down, with one elderly woman saying, "we want our children and brothers, kill us with them and get it over with."
Standing in front of the coffins of the victims, Coptic Orthodox Pope Tawadros II comforted mourners and chastised those responsible for the bombing.
"Do not believe that you have achieved anything," he said.
"The pain you caused to all our hearts, to the hearts of Egypt, to the heart of every human in the entire world, this pain will be set upon you and it will fill you. You will live in destruction.
"You will see that what your blood-stained hands have done will reflect on you."
The emotional speech was dotted with ululations, more traditionally heard at weddings, performed on this occasion to celebrate the ascension of martyrs to heaven.
Cardboard placards bearing the names of those who died lined the wooden walls of the church.
Screams and wailing were heard throughout the Pope's talk and as the coffins were taken to the funeral procession to be led by el-Sisi.
On Sunday, el-Sisi condemned the attack and declared a three-day period of national mourning.
The Grand Mufti, the highest official of religious law in Egypt, also condemned the "deplorable terrorist attack" on the cathedral.
"Attacking churches whether by demolition, bombing, killing those inside, or terrifying ... secure people are prohibited in Islamic Sharia," Sheikh Shawky Ibrahim Abdel-Karim Allam said.
He called for unity against "black terrorism that tries to instigate sectarianism and sedition among the two wings of Egypt -- Muslims and Christians -- in a bid to weaken the nation."
The Grand Mufti and Pope Francis also extended their condolences to Pope Tawadros ll of the Coptic Orthodox Church of Alexandria.
Hundreds of demonstrators gathered outside the cathedral Sunday to voice their anger at police and some pro-government television anchors, according to state-run Al-Ahram.
They called for the resignation of the interior minister, Magdy Abdel Ghaffar.
Protesters chanted: "This time won't pass, even if we all die. ... This is not sectarian strife, let's get the world to hear."
Sunday's explosion came just two days after two bombs
killed six police officers and a civilian in Giza's Haram district, on the street leading to the city's famed pyramids.
Hassm, the group that claimed the deadliest bomb on Friday, condemned Sunday's attack and blamed the government for it. Responding to the criticism, el-Sisi said his government is doing everything it is required to do to keep people safe.
"You don't know the size of the success we achieved even in fighting terrorism," el-Sisi said Monday. "Don't say this is a security flaw."
No one has claimed responsibility for this bombing, the deadliest attack on Copts since 2011.
Copts facing persecution
Copts face persecution and discrimination that has spiked since the toppling of Hosni Mubarak's regime in 2011. Dozens have been killed in sectarian clashes. There is also little Christian representation in Egypt's government.
Coptic Christians make up about 10% percent of Egypt's 91 million residents. They base their theology on the teachings of the Apostle Mark, who introduced Christianity to Egypt, according to St. Takla Church in Alexandria, the capital of Coptic Christianity.