Egyptian investigators on Thursday spent more than four hours briefing Italian counterparts on their so-far inconclusive probe into the torture and murder of an Italian student in Cairo that threatens to derail close ties between the two countries.

A team of five Egyptian prosecutors and police has come to Rome with a 2,000-page file on the probe into the murder of Giulio Regeni, a 28-year-old PhD student at Cambridge University.

Their work, which Egyptian media described as ongoing, was presented to Rome prosecutor Giuseppe Pignatone and senior security officials in a closed-doors meeting at a police training college.

Italian officials are not convinced everything is being done to bring Regeni's killer or killers to justice and have warned of consequences if the Egyptians do not present a credible account of everything they know about his gruesome fate.

The talks will continue on Friday. To date there has been no attempt by the Egyptian team to contact Regeni's family, their lawyer said.

The case is a testing one for Italian Prime Minister Matteo Renzi, who has fostered a close relationship with Egypt's military-backed president, Abdel Fattah al-Sisi, but is under pressure to respond to public anger over the case.

"The relationship is a huge deal for Italy but Egypt has burnt most of its credit in the last two months in a not very smart way," said Mattia Toaldo, of the European Council on Foreign Relations (ECFR) in London.

Regeni disappeared in central Cairo on January 25.

His body was found on the outskirts of the city on February 3 bearing the signs of torture which, an autopsy concluded, had been inflicted over several days.

Media coverage of the case has focused international attention on other disappearances and rights abuses in Sisi's Egypt.

Regeni's family have threatened to release pictures of his mutilated body to keep the pressure on over his death.

Their stance was praised on Thursday by the mother of Khaled Said, whose 2010 killing by Egyptian police contributed to the wave of anger that led to the Arab spring uprising of 2011.

"I thank you for standing with us and caring about torture cases in Egypt," Laila Marzouk said in a video posted on YouTube.

At the end of last month, Egypt publicly announced police had killed four members of a criminal gang they suspected of murdering Regeni.

That version of events was greeted with scepticism in Italy, where many suspect the murder was the work of elements in the security services - a theory Cairo dismisses as without foundation.

Italy has warned of "immediate and proportionate" action if the Egyptian delegation does not provide satisfactory answers.

Investigators in Rome want to see Regeni's mobile phone records and CCTV images from the neighbourhood in which he was abducted. Unconfirmed reports from Egypt said some of these elements had been handed over on Thursday.

Rome also wants to know if and why Regeni was under surveillance prior to his abduction. The student had been researching independent labour unions in Egypt.