It comes after Egyptian officials briefed their Italian counterparts on the investigation into the killing. Italian Foreign Minister Paolo Gentiloni tweeted (in Italian) that Italy wanted "one thing only: the truth about Giulio". Rights groups have suggested security forces were to blame, but Egypt says a criminal gang was behind his murder.
Mr Regeni, 28, disappeared on his way to meet a friend on 25 January. His body, mutilated and showing signs of torture, was found in a ditch on 3 February.
Correspondents say that there is a feeling in Italy that the Egyptian authorities are not moving fast enough in their investigation. Prime Minister Matteo Renzi has said Italy will not settle for what he called a "convenient truth".BBC News