Giulio Regeni, a Cambridge University PhD student who was researching Egyptian labour movements, disappeared on January 25 and his badly mutilated body was found a week later.
Italian media have suggested he may have been detained by Egyptian security forces, something the interior ministry has strongly denied.
The ministry said it had not yet determined who abducted Regeni, but "available information suggests all possibilities."
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"These include a criminal motive or personal revenge," the statement said, adding the ministry was cooperating with Italian investigators in Cairo.
Regeni went missing on the fifth anniversary of the start of the uprising which overthrew longtime autocrat Hosni Mubark.
Police had been deployed across the city to prevent demonstrations.
The interior ministry has been on the defensive over a string of deaths in police custody and other abuses that prompted the interior minister to apologise to the country this week.