Accounts of Friday's events are conflicting; Egypt's Interior Ministry cites just one attacker - a revision of initial reports which claimed that two attackers were involved and that 12 people had been killed.
The Islamic State has claimed responsibility for the attack, along with several other terrorist attacks on Coptic Christians over the a year ago in in Egypt, resulting in the deaths of more than 100.
Police have stepped up security measures around churches ahead of the Coptic Christmas celebrations on January 7, deploying officers outside Christian places of worship and setting up metal detectors at some of the bigger churches.
The Islamic State has claimed responsibility for the shooting rampage on Friday via its Amaq news agency.
The police had said it shot dead the terrorist before he could break into the church.
A witness who did not want to give his name said the policeman was killed while he was closing the church gate to stop the gunman getting in.More news: Serena Williams' comeback at Mubadala World Tennis Championship ends in defeat
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Security sources said on Saturday that the captured injured attacker of Helwan's Church of Great Martyr Mina underwent successful surgery to remove bullets from his foot.
Pope Francis prayed for the victims of Islamic State attacks on a Coptic Church and Christian business in Egypt as part of his traditional Sunday Angelus address, according to Crux.
Egypt's Coptic Christians make up about 10 per cent of the country's 93 million people, and are the largest religious minority in the region. President Abdel-Fattah el-Sissi has personally chaired meetings with his top security chiefs in recent days to discuss security during New Year's Eve and the Orthodox Christmas.
The ministry said security forces had "immediately dealt with the [attacker] and arrested him after he was wounded".
The Interior Ministry added that at least five others were injured, with two of them being in a serious condition.
TV footage showed one attacker wearing a bulky ammunition vest lying on a street. They added that the exchange of fire continued for around 20 minutes. "There was more than one attacker", Mohammed Hussein Abdelhadi, who lives close to the church, told Reuters.