Security forces reportedly shot and killed one of the attackers who was carrying an undetonated explosive belt after an exchange of fire and another was arrested.
The gunman was also killed, along with at least one police officer, officials said.
Coptic churches in Egypt are often attacked.
The gunman had opened fire outside the church, wounding five security guards, and tried to storm the building when police shot him dead, the officials said. Police have been stationed outside churches and in nearby streets across Cairo.
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Days ahead of the New Year's Eve, Egypt witnessed a deadly attack on the Coptic church of the Great Martyr Mina in Helwan, in a Cairo suburb, during Christmas ceremonies on Friday. It was the latest attack targeting Egypt's embattled Christian minority.
Police have stepped up security measures around churches ahead of Coptic Christmas celebrations on January 7, deploying officers outside Christian places of worship and setting up metal detectors at some of the bigger churches.
Security forces went on high alert for Christmas and New Year celebrations.
Two gunmen opened fired outside the Marmina Coptic Orthodox church in Helwan, a neighborhood in south Cairo, Khaled Megahed told reporters. The officials requested anonymity because they were not authorized to brief the media. Al Arabiya TV channel reported that one of the accomplices of the terrorists fled the scene.
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Also, the Italian Embassy in Egypt strongly condemned Friday's heinous attack in Helwan.
A video circulated on social media after the attack apparently shows the dead gunman on the ground.
Police later cordoned off the crime scene as onlookers crowded around the church, while a forensics team combed the area.
Egypt's Christian minority has been targeted by Islamic militants in a series of attacks since December 2016 that left more than 100 dead and scores wounded.
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Radtke says the increased cases this season are partly caused by a mismatch between the vaccine and the flu strain circulating. It also maintains that an annual flu vaccine is the the first and most important step in protecting against flu viruses.