The Coptic Church said the gunman first shot at a Christian-owned shop 4km away, killing two people, before proceeding to the Mar Mina church in the southern Cairo suburb of Helwan.
The Interior Ministry said he opened fire at the entrance to the site and tried to throw an explosive device.
According to Interior Ministry and Coptic Church accounts, 11 were killed in all, including a policeman at the church.
The health ministry had said earlier that five people were wounded, including two women who were in serious condition.
The Church said a young woman had died later from her wounds.
Earlier reports by security sources and state media said at least two attackers were involved, and that one was shot dead and another fled the scene. The interior ministry did not explain the reason for the different accounts.
It also said there was a separate attack on a shop in the same neighbourhood of Helwan that killed two Copts.
The ministry added that investigators had identified the gunman and that he had carried out several attacks since last year.
Samir Gerges, a witness, said people inside the church closed the gates when the shootout began but bullets from the gunfire still entered the building.
Mr Gerges said he was walking in a nearby street when the shooting happened. He saw people running and some of them went to hide from the gunfire inside a nearby restaurant.
Raouth Atta, 40, was attending prayers inside the church when the shooting took place.
“Once the gunfire was heard, the gates were closed immediately,” she said. “People were terrified and wanted to check on their families in other buildings of the church. We stayed inside for 30 minutes before we were able to get out.”
Ms Atta said that once she was let outside the building she saw blood scattered everywhere.
A video circulated on social media after the attack apparently shows the dead gunman on the ground.
Authorities have closed off the area around the church, and a joint funeral for eight of those killed was held on Friday evening at the Virgin Mary church in Helwan.
The Christian minority, which makes up 10 per cent of the Egyptian minority, has been regularly targeted by Islamist extremists such as Isis in recent years.
Just last week, hundreds of Muslim demonstrators stormed an unlicensed church south of Cairo wounding three people. The demonstrators shouted anti-Christian slogans and called for the church’s demolition, the diocese in the area said at the time. The demonstrators destroyed the church’s contents and assaulted Christians inside before security personnel arrived and dispersed them.
Meanwhile earlier this year at least 43 people were killed in twin bombings in Coptic churches in the cities of Alexandria and Tanta, while they gathered to celebrate Palm Sunday.
Children were among the 28 people killed when gunmen opened fire on a bus travelling to a Coptic monastery in Minya province in May.
The Coptic sect, a branch of Orthodox Christianity, has lived in Egypt and other parts of north-east Africa such as Ethiopia for thousands of years, but have recently been targeted by hardline Sunni Arabs Islamists, including Isis, who regard them as “infidels” helping the West wage war on Muslims.
In response to the Minya bus attack, the Egyptian military launched an air strike against what it said were militant training facilities in Libya.
Muslim leaders including the Grand Mufti of Egypt and the grand imam of al-Azhar, Egypt’s 1,000-year-old centre of Islamic learning, condemned that attack as the act of “brutal terrorism” and called on Egyptians to unite.
Additional reporting by agencies
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