More than 3,000 people attended a private funeral for the 28-year-old in his home town of Fiumicello in northeastern Italy, nine days after his torture-scarred body was found dumped in a ditch on the outskirts of the Egyptian capital.
A two-hour service in the town's sports hall culminated in a poignant message from his mother Paola Regeni, read on her behalf by a friend of Giulio's.
"Thank you Giulio for having taught me so many things. The energy of your thinking will stay in my heart. Your thinking about how to love, how to understand and how to build tolerance. I love you. Mamma."
The Egyptian coptic priest who had blessed Regeni's corpse following its discovery in Cairo had earlier said Regeni's death could serve to save other lives, referring to the biblical story of Barabbas, the man chosen by a mob to be spared crucifixion ahead of Jesus Christ.
"Giulio is the scapegoat who will free the Barrabas that we do not yet know," said Father Mamdua, who was invited to Italy for the service by the Regeni family.
Fiumicello mayor Ennio Scridel described what had happened to a popular son of the sleepy town in the northeastern corner of Italy as "an unimaginable nightmare".
"There is nothing that can make what happened understandable, when man turns into a beast. This story does not finish here," he said.
Hours earlier Renzi had said Egypt was cooperating with Rome's demand that Italian investigators be fully involved in the investigation into the death of the 28-year-old.
"For the moment, all our requests have been met and above all we have demanded that every element should be put on the table in order that the truth can be established and those really responsible can be detained," Renzi told Radio Anch'io.
"This has been a tragic event," he added.
"I extend my condolences to Giulio's family and I say that we have told the Egyptians: friendship is a precious asset but it is only possible on the basis of truth."
The Cambridge University PhD candidate researching labor issues disappeared heading to an appointment 25 January, when security was intense in the capital Cairo for the fifth anniversary of Egypt's 2011 uprising.
Regeni's tortured body was found on 3 February. Italy is demanding Egypt find his killers.