The request was turned down on the basis that Egyptian law forbids the presence of foreign magistrates during judicial activity.
Regeni's parents, Claudio and Paola, were informed of the refusal during a meeting on Friday with Rome chief prosecutor Giuseppe Pignatone and his assistant Sergio Colaiocco.
Cairo prosecutors have, however, sent their Italian counterparts a second report on testimonies from the seven policemen who questioned Regeni before his death.
Regeni, 28, went missing in the Egyptian capital on January 25, 2016, on the heavily policed fifth anniversary of the uprising that ousted former president Hosni Mubarak.
His severely mutilated body was found eight days later in a ditch on the city's outskirts.
Egypt has denied speculation its security forces, which are frequently accused of brutally repressing opposition, were involved in the death of the University of Cambridge doctoral student.
Regeni was researching street vendors' trade unions, a sensitive topic, at the time of his death.
Egyptian and Italian prosecutors have been working on the case together, but Rome is yet to send a new ambassador to Cairo in protest at the lack of progress made so far on the case.
"Italy has mourned the murder of one of its studious young people, Giulio Regeni, without full light being shed on this tragic case for a year, despite the intense efforts of our judiciary and diplomatic personnel," Italian President Sergio Mattarella said on the anniversary of Regeni's disappearance.
"We call for broader and more effective cooperation so that the culprits are brought to justice."
Italian Premier Paolo Gentiloni expressed his support for Regeni's family and said his government was determined to expose the truth.
A video recently surfaced in which the head of the Cairo street traders' union, Mohammed Abdallah, secretly recorded Regeni as he asked him questions about the union.
Abdallah said he was doing his patriotic duty because he believed Regeni was a spy.
Egypt has come up with several explanations for Regeni's death, ranging from a car accident to a kidnapping, all of which have been dismissed by Italy.
Suspicion has fallen on seven members of the Egyptian police and intelligence services who used Abdallah as an informant and were responsible for wiping out an alleged kidnapping gang.
Regeni's personal documents were reportedly found in the house of an alleged gang member’s sister.
With ANSA
