The attack attempt was thwarted amid high security measures taken by the Ministry of Interior nationwide ahead of Christmas celebrations in Egypt.
One attacker was killed and another has fled the scene on a motorbike, the statement said.
He announced that a recent victim of Helwan church attack named Nermin Sadek, 35, died as a result of her wounds. No group has yet claimed responsibility for the attack.
The assault came a little more than a month after militants killed 311 worshippers inside a mosque in Sinai, the deadliest attack by militants on civilians in Egypt's modern history.
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I remember being on tour and being in the United Kingdom at the time when the child died, and just being really sad about it all. We all study music and we would listen to her songs and watch her performances. "I knew why I wanted to make myself disappear".
But because the group provided no evidence it is unclear whether Islamic State was involved or whether the gunman was inspired by the group, or if there is no connection. But an eyewitness says that other men are on the run.
Eyewitnesses said that the two masked militants on a motorcycle entered the street leading to the western side of the church, and then got off and targeted the security post outside the church. Attacks against Coptic communities have especially increased during Christian holidays.
Two police officers were among those killed, reports said.
Around 10% of Egypt's population is Christian, and the majority belong to the Coptic Orthodox Church.
Omar Ashour, a visiting professor of security studies at the Doha Institute, told Al Jazeera the attack was part of an "ongoing crisis" in Egypt. They say the exchange of fire also injured three other people.
The attack came amid tightened security around churches and Christian facilities ahead of the Coptic Orthodox Christian celebrations of Christmas on January 7. Sirens were heard in central Cairo as the incident was first reported.