The blaze started during a Sunday morning service in the Abu Sifin church in the city of Giza where about up to 1,000 people had gathered.
The fire blocked an entrance to the church, causing the stampede, two security sources said, adding that most of those killed were children.
"People were gathering on the third and fourth floor, and we saw smoke coming from the second floor. People rushed to go down the stairs and started falling on top of each other," said worshipper Yasir Munir.
"Then we heard a bang and sparks and fire coming out of the window," he said, saying he and his daughter were on the ground floor and able to escape.
Electrical fires are not rare in Egypt. In late 2020, a fire at a hospital treating COVID-19 patients killed at least seven people.
In a statement, the Interior Ministry said a forensic examination showed that the fire began in the second floor air conditioning as a result of an electrical malfunction.
Smoke inhalation was the main cause of death, it said. Families of those who died will receive 100,000 Egyptian pounds ($A7,325), according to a cabinet statement.
Giza, Egypt's second-largest city, lies just across the Nile from Cairo.
"I offer my sincere condolences to the families of the innocent victims that have passed on to be with their Lord in one of his houses of worship," said Egyptian President Abdel Fattah al-Sisi in a tweet.
Maher Murad said he left his sister at the church after prayers.
"As soon as I got away from the church by only 10 metres, I heard the sound of screaming and saw thick smoke," he said.
"After the firefighters doused the fire, I recognised my sister's body. The bodies were all charred, and many of them are children who were in a nursery room in the church."
"I don't know if it was an electrical fire or what happened, but there were kids and old people, we saved whom we could save," said Kirollos, who was speaking from a hospital where he was being treated for injuries.
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