The interior ministry said in a statement a van used by the criminals had been found containing an unidentified corpse with a bullet wound.
Regeni's belongings were then found at the home of one of the suspects' sister.
"Italian security has been has been notified about the results," the statement said.
The Cambridge University graduate student's mutilated body was found in a ditch on the edge of Cairo in January nine days after he disappeared.
Regeni was the only foreigner reported missing recently in Egypt.
Earlier Thursday, the ministry said: "The security forces on Thursday managed to track down a gang in new Cairo that used to pose as policemen. It specialised in abducting foreigners and robbing them.
"There was an exchange of fire with the police and all members of the gang were killed," it added without giving a toll.
Italian media and Egyptian opposition figures suspect Regeni was abducted and killed by elements of the Egyptian security forces, an allegation Cairo has steadfastly denied.
Egyptian officials have assured Italy of a "transparent investigation" into Regeni's murder, with President Abdel Fattah al-Sisi vowing to "get to the truth" of the case.
Regeni was in Cairo doing research for his doctoral thesis on Egyptian labour movements.
