Rome slams Egypt's clearing police in Italian's murder
The decision announced on Wednesday came nearly three weeks after Italian prosecutors said they planned to charge four Egyptian security officers over the torture and death of Regeni.
The Cambridge University graduate was in Egypt researching trade unions, when he was kidnapped in January 2016 and his mutilated body later found on the outskirts of Cairo.
"The declarations of the Egyptian public prosecutor's office are unacceptable," the Italian foreign ministry said in a statement.
It said it would "continue to work at all levels, including through the European Union, for the truth about Giulio Regeni's brutal murder to finally emerge".
"We hope the Egyptian public prosecutor shares this insistence on the truth and will extend all necessary collaboration to the Rome prosecutor's office," it added.
In his statement, public prosecutor Hamada al-Sawy said he had no intention of "pursuing a criminal case in the murder, abduction and torture of Giulio Regeni because the perpetrator is unknown".
Investigators would continue to seek the identity of the murderer but the prosecution has "ruled out" any charges "against the four officers and a fifth policeman" in connection with the case, he said.
Regeni's death sparked outrage in Italy and strained diplomatic relations between the two countries, with Italy's government accusing Egyptian authorities of non-cooperation.
On December 10, Italian public prosecutor Michele Prestipino told a parliamentary commission in Rome there were "elements of significant proof" implicating Egyptian policemen.
"We are going to ask to begin a criminal action concerning certain members of the Egyptian security services," he said.
"We owe it to the memory of Giulio Regeni."
Regeni had been researching the sensitive topic of labour organisations in Egypt when he disappeared. He had also written articles critical of the government under a pen name.