ROME (Reuters) - Italy said on Tuesday it would take "immediate and proportionate" measures against Egypt if the Cairo government did not fully cooperate in uncovering the truth over the murder of an Italian student.

Giulio Regeni vanished from the streets of Cairo on Jan 25. His body, showing signs of extensive torture, was discovered in a ditch on the outskirts of the Egyptian capital on Feb. 3.

"If there is not a change in tack (by the Egyptian authorities), the government is ready to react, adopting measures that are both immediate and proportionate," Foreign Minister Paolo Gentiloni told parliament.

Gentiloni did not elaborate, but the head of parliament's human rights committee said last month that the government should recall Italy's ambassador to Cairo and declare Egypt unsafe for visitors if the investigation went nowhere.

Regeni's murder has brought relations between the two countries to one of their lowest points, with Italian officials openly ridiculing different versions of Regeni's death put forward by Egyptian investigators, including an initial suggestion that he had died in a traffic accident.

Gentiloni said a change of tack "means not accepting twisted and convenient truths. It means finding out who was responsible for having probably put Giulio Regeni under surveillance before he disappeared." He also called for a more pro-active investigation by Egypt and more cooperation with Italy.

After a series of delays, Egyptian investigators are due to hold talks with Italian magistrates in Rome on Thursday and Friday, Gentiloni said.

Human rights groups have said torture marks on Regeni's body indicated he died at hands ofEgyptian security forces, an allegation Cairo has repeatedly denied.

The case has raised fresh questions about accusations of police brutality in Egypt, a strategic ally of the West and an important trade partner for Rome.

(Reporting by Philip Pullella; Editing by Crispian Balmer)