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Egypt arrests four in connection with Cairo church bombing
Among those detained are Karam Ahmed Abdel-Aal Ibrahim, one of two suspected plotters, and three others who were plotting similar acts elsewhere, the ministry said in a statement.
Mohab Mostafa el-Sayed Qassem, thought to be the group's leader, is still at large, it added.
Egyptian authorities allege that Qassem received logistical support, financial backing and instructions on the attack by Muslim Brotherhood leaders in Qatar.
The Brotherhood, which has been banned and driven underground during President Abdel Fattah al-Sisi's time in office, has denied involvement.
While Egyptian authorities have often blamed the Brotherhood for various attacks committed throughout Egypt, it was the Islamic State group who claimed responsibility for the bombing at the Saint Peter and Saint Paul church.
According to the group's affiliated media outlets, the suicide bomber went by the nom de guerre Abu Abdallah al-Masri.
Wednesday saw the death toll of the December 11 suicide bombing attack rise to 27, after a 63-year-old woman succumbed to her wounds, Egypt's health ministry said.
Eleven people still remain in hospital, it added.
At present, Egyptian security forces are struggling to control an Islamist insurgency that has gained a foothold in the country since 2013.
Groups in the northern Sinai region, some of whom are affiliated to IS, have launched attacks against police, army positions, public officials and civilians.