The lawyer for the family of Giulio Regeni, the Italian doctoral student murdered in Egypt in 2016, said she has a list of 20 additional suspects, which she called “20 names of men who should start being afraid”.

At a press conference in Rome on Wednesday, Alessandra Ballerini said: “I find hard to believe that the Egyptian president, Abdel Fatah al-Sisi, was not aware of what was going on to Giulio Regeni. It’s impossible he didn’t know anything about this.” She said the list was compiled over the course of her almost three-year-long investigation with a legal team in Egypt.

Regeni disappeared on 25 January 2016, and his body was found on an outlying Cairo desert road on 4 February that year bearing signs of extreme torture. The desert highway his corpse was found on joins Egypt’s capital with Alexandria, and passes close to a building used as a detention facility by Egypt’s National Security Agency (NSA).

His parents, Paola and Claudio Regeni, told the press conference: “We are not giving up. Egypt must know that we are not going to give up. Egypt is jeopardising its relationship with Italy because in Egypt an Italian student has been kidnapped, tortured and killed – [as] said by the president of the Italian chamber of deputies, Roberto Fico – and we will continue to put at risk our relationship with Egypt till we finally uncover the truth.’’

Earlier this week Roman prosecutors formally placed under investigation five members of Egypt’s NSA as suspects in the alleged murder of the Italian researcher. They were the first Egyptians to be named by the Italians in connection with the case after almost three years.

The Italian authorities formally opened an investigation into Maj Gen Sabir Tareq, Maj Sherif Magdy Abdel Aal, Col Acer Kamal and Col Hesham Helmy of the NSA, as well as officer Mahmoud Najem. The five are believed to have participated in Regeni’s disappearance, according to Rome’s deputy chief prosecutor, Sergio Colaiocco. They are all suspected of kidnapping the Italian student.

According to Associated Press, Tareq was a high-ranking NSA officer at the time of Regeni’s abduction and murder, and has since retired. Helmy oversaw the Giza neighbourhood of Dokki, where Regeni lived, while Kamal headed a department focusing on street-level discipline. Aal was the head of a team that had Regeni under surveillance before his disappearance. “At least one of the officials has been reassigned to a remote province,” it added.

The NSA is Egypt’s primary domestic intelligence body, a cornerstone of the police state under both Sisi and in its previous incarnation as the State Security Investigations Service under the autocratic former president Hosni Mubarak.

Italy’s accusation about the NSA’s involvement in Regeni’s murder gives some indication as to why an academic specialising in the politically sensitive subject of unions was a target. “Since March 2015, the NSA has appeared to be the lead agency responsible for arresting, detaining and building criminal cases against political suspects, holding many in incommunicado detention and subjecting them to enforced disappearance and torture,” said Amnesty International in a 2015 report.

Egypt rejected Italian efforts to name NSA agents as suspects in the Regeni case earlier this week. “Egyptian law does not recognise what is called ‘the record of suspects’,” said the country’s State Information Service, citing an anonymous member of the judiciary. Egypt’s ministry of foreign affairs has not responded to repeated requests for comment on the issue by the Guardian.

Italy’s parliament previously suspended relations with Egypt after initial reports of the list of suspects. But at Edex, Egypt’s first international defence exhibition, which showcased military hardware and weapons from around the world, little of this tension was on display. “If we have permission to export guns here, it means things remain the same,” said Jarno Antonelli of Beretta, which supplies pistols to the Egyptian military and police.

“We have been waiting three years,” said the minister of the interior, Matteo Salvini. “I want to maintain good relations with Egypt and I will do everything to have good economic, cultural, commercial and social relations with a friendly country, but as an Italian I expect [from Egypt] names and surnames.”