A ministry statement today says the three were planning to carry out other "terrorist operations" and that one of the men was found with weapons, including explosives.
Egypt's Islamic State affiliate has claimed responsibility for the bombing, though authorities have blamed the banned Muslim Brotherhood group.
Earlier, three men and a woman were arrested over the attack.
The ministry has said the attacker belonged to a terror cell founded by an Egyptian doctor and funded by Brotherhood leaders living in exile in the Gulf Arab nation of Qatar.
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