Egypt has bowed to Italian pressure to reopen its investigation into the death of Cambridge student Giulio Regeni, Italian Interior Minister Angelino Alfano has said.

Italy had objected to Egypt's claim on Thursday that police had found Regeni's killers after four alleged gang members were shot dead in a raid on an apartment in which Regeni's CamCard and passport were found.

"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," the foreign ministry said in a statement.

"There was an exchange of fire with the police and all members of the gang were killed."

Regeni's family expressed their anger at Egypt's handling of the case and their claims over events in the apartment, accusing them of "outrageous staging".

"We are hurt and bitter at yet another attempt at misdirection by the Egyptian authorities over the barbaric killing of our son Giulio," La Repubblica newspaper quotes them as saying.

Italian prosecutors expressed their scepticism at this version of events. A seven-member Italian team has been in Egypt investigating the student's death for nearly two months, but the evidence they have seen "is not adequate in clarifying the death of Giulio Regeni and in identifying those responsible for the homicide", Rome's Chief Prosecutor, Giuseppe Pignatone, said in a statement.

Pignatone called on Egyptian investigators to provide the team with all the evidence they have requested. He arrived in Egypt on 14th March to put further pressure on Egyptian authorities.

Giacomo Stucchi, president of Italy's parliamentary secret service committee, claimed Egypt was providing "garnished truth" over the student's murder, accusing investigators of insulting Regeni's memory and showing "a total lack of respect for Italy".

"Italy insists: we want the truth," Foreign Minister Paolo Gentiloni said in a tweet on Friday.

Alfano told Italian newspaper Corriere della Sera on Sunday: "It is important that in the face of our emphasis on the quest for truth, the Egyptians changed tack in a few hours and told us that their investigations are continuing. 

"Our investigators should be directly involved, participating in questioning and evidence gathering.... Our input is essential.

"I repeat to Giulio’s parents and to the Italian public that the Italian government will get the name of the murderers."

Students, politicians and university authorities in Cambridge have all joined widespread international calls for a "credible investigation" into the student's death.

Human rights observers suggested that the signs of torture on Regeni's mutilated body, including cigarette burns and multiple stab wounds, indicated the authorities' involvement in his death.

The New York Times had previously claimed that CCTV footage showed Regeni being led away "by two men believed to be Egyptian security agents" had been deleted, further stoking suggestions of foul play.

The Egyptian authorities strongly deny any suggestion that they were involved in the student's death.

Giulio Regeni was a visiting scholar at the American University in Cairo, researching trade unions and labour rights in Egypt, a topic analysts consider sensitive in the country.

Regeni disappeared in Cairo on 25 January, exactly five years after Hosni Mubarak was ousted from power. His body was found on a roadside nine days later.