By Steve Scherer

ROME (Reuters) - Italy on Wednesday said Egyptian investigators should hand over the evidence they had uncovered in the death of an Italian graduate student who was tortured and killed in Cairo.

Giulio Regeni, 28, disappeared in January and his battered body was found in a ditch at the beginning of this month. Egypt invited Italian investigators to take part in the probe, but judicial sources in Rome say the collaboration has been limited.

"Cooperation with our investigative team can be and must be more effective. It cannot be only formal," Italian Foreign Minister Paolo Gentiloni said during parliament's question time.

Regeni had been researching independent trade unions in Egypt and written articles critical of President Abdel Fattah al-Sisi's government, prompting speculation that he was killed in the hands of Egyptian security forces.

Earlier on Wednesday, Egypt's Interior Ministry said there were still several possible scenarios for the murder, but it did not mention the involvement of security forces as a hypothesis.

Gentiloni said Italy wanted access to specific evidence.

"Italian investigators must have access to audio and video documentation, medical test results and the legal documents from the Giza prosecutor's office," he said.

Some Egyptian, Italian and international media have speculated that Regeni was killed by the police or secret services.

Egypt's interior ministry said possible motives included criminal activity or the desire for revenge "due to personal reasons."

Regeni had "many relationships with people near where he lives and where he studied," it said in a statement carried by state news agency MENA.

In the Italian parliament, Gentiloni referred to the investigative developments "evoked this morning" as "improbable" -- a sign of increasing strain between the two countries over the mysterious death.

Italy has significant economic interests in Egypt, including the development of the giant Zohr gas field off the North African coast being developed by Italy's state oil producer Eni.

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Egypt's interior and foreign ministers have dismissed the notion that security forces were behind Regeni's murder. Human rights groups accuse Egypt's Interior Ministry of widespread abuses, allegations it denies.

A senior source at Egypt's forensics authority told Reuters that Regeni, a graduate student at Britain's Cambridge University, had suffered seven broken ribs, with signs of traumatic injuries all over his body.

A second autopsy in Italy "confronted us with something inhuman, something animal", Italian Interior Minister Angelino Alfano said.

(Additional reporting by Mostafa Hashem and writing by Ahmed Aboulenein in Cairo; Editing by Michael Georgy, Crispian Balmer and Raissa Kasolowsky)