ROME (Reuters) - The parents of Italian graduate student Giulio Regeni, who was tortured and killed in Cairo, demanded on Tuesday a tough response from Rome if Egypt fails to uncover the truth behind their son's murder.

Giulio's mother, Paola Regeni, said she might release a photograph of her son's body to show the world what had happened to him in Egypt if his murderers were not revealed.

"I only recognized him because of the tip of his nose. As for everything else, it was no longer him," she said in the first news conference the family has given since Giulio's battered body was found in a roadside ditch on Feb. 3.

The 28-year-old student went missing on Jan. 25 and human rights groups have said the signs of torture indicated he had been killed by Egyptian security forces, an allegation Cairo has vigorously denied.

Egyptian officials are due in Italy on April 5 to discuss the investigation. "If April 5 proves to be a wash-out, we expect a strong response from our government, a really strong one," PaolaRegeni said.

The head of parliament's human rights committee, Luigi Manconi, who also took part in the news conference, said the government should recall Italy's ambassador to Cairo and declare Egypt unsafe for visitors if the investigation went nowhere.

"Relations should not be broken, but they should face a particularly significant revision," said Manconi, a member of Prime Minister Matteo Renzi's Democratic Party. Giulio Regeni's father, Claudio, said he supported this call.

Last week, Egyptian police said they had discovered Regeni's bag and passport following a shootout with a criminal gang. Italian officials dismissed the story and Regeni's family said it was clear Giulio had not been killed for criminal gain.

The family lawyer, Alessandra Ballerini, said the Italian autopsy showed that Regeni was alive until Feb. 1 or 2 and that there had never been a ransom bid or money stolen from his bank account in the days after his disappearance.

"Whatever the truth, it is clearly very uncomfortable for the (Egyptian) regime," she said.