Egypt's chief prosecutor has denied allegations that the police tortured a detained human rights activist and researcher during interrogations.

Police detained Patrick George Zaki, an Egyptian student at the University of Bologna in Italy, after landing in Cairo earlier this month for what was supposed to be a brief visit home.

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Zaki told his lawyers he has been beaten, subjected to electric shocks, threatened and questioned about his work and activism, according to The Egyptian Initiative for Personal Rights, a Cairo-based human rights group that previously employed him as a gender rights researcher.

The researcher's lawyer Huda Nasrallah also told The Associated Press news agency that Zaki repeated his torture allegations on Saturday during a court hearing to appeal against his detention. The court rejected the appeal. Zaki is being held while prosecutors investigate claims of disseminating false news and calling for unauthorised protests, among other allegations.

But in a two-page statement on Sunday, the office of General Prosecutor Hamada el-Sawy said Zaki did not report that he was "harmed or violated during his arrest or detention" when he spoke to the public prosecution on February 8, the day after his arrest.

"The public prosecution also did not observe any visible injuries that could be useful to the investigations, and that the defendant responded denying the existence of any injuries to his body," the statement read.

As evidence in the case against Zaki, Egypt's national security agency provided 10 pages printed from a Facebook account carrying the name Patrick George Zaki. The statement described it as "inflammatory material against the state institutions and figures".

It said Zaki denied the claims against him, and that the prosecutor's office ordered him to remain in custody pending further investigations.

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Egypt outlawed all unauthorised protests in 2013, months after President Abdel Fattah el-Sisi, then defence minister, led the military's removal of the country's first democratically elected president, Mohamed Morsi, following mass protests.

Zaki's case has sparked alarm among human rights groups and has also rattled Italy amid fears of a repeat of the case of murdered Italian doctoral student Giulio Regeni.

Regeni's body was found on a roadside on the outskirts of Cairo in 2016 showing extensive signs of torture.

After four years of investigation, no one has been arrested or charged over the killing of the 28-year-old, despite months of presumed cooperation between Egyptian and Italian prosecutors. Italy is still pressing Egypt to speed up the investigation.