The blaze on Sunday, blamed on an electrical fault, hit the Abu Sifin church in densely populated Imbaba, a working-class district west of the Nile River, part of Giza governorate in Greater Cairo.
Hundreds gathered to pay their respects in and around the two Giza churches on Sunday evening where clergymen prayed for the victims.
Pallbearers pushed through crowds of weeping mourners who reached for the coffins, including that of a priest at the church, Father Abdel-Messih Bekhit.
The Egyptian Coptic Church and the health ministry reported 41 dead and 14 injured in the blaze before emergency services brought it under control.
Witnesses to the fire on Sunday morning described people rushing into the multistorey house of worship to save those trapped, but the rescuers were soon overwhelmed by heat and deadly smoke.
Copts are the largest Christian community in the Middle East, making up at least 10 million of Egypt’s 103 million Muslim-majority population.
A statement from the public prosecutor’s office indicated that asphyxiation caused the deaths, as there were “no visible injuries”.
The interior ministry announced “forensic evidence revealed that the blaze broke out in an air-conditioning unit on the second floor of the church building” which also houses social services.
President Abdel Fattah el-Sisi wrote on his Facebook page that he had “mobilised all state services” in response. He later said he had “presented his condolences by phone” to Pope Tawadros II, the head of the Coptic Orthodox Church.
He also directed the Armed Forces Engineering Authority to “take over the reconstruction and renovation” of the church, the presidency announced in a statement.
A statement from the office of United Nations Secretary-General Antonio Guterres offered his “deepest condolences” to the families of the victims.
Accidental fires are not uncommon in the sprawling megalopolis of Cairo, where millions live in informal settlements amid dilapidated and poorly maintained infrastructure.