Hundreds of Muslim Brotherhood supporters have chanted anti-military slogans outside Cairo University in the capital to defy Egypt's army-backed government.

On Tuesday, supporters of deposed President Mohamed Morsi had urged university students to protest against the army following the violence on Sunday, one of Egypt's bloodiest days since the military ousted the leader on July 3.

The death toll from Sunday's unrest rose to 57, state media said, with 391 people wounded.

"We are here standing against the coup," said Enas Madkour, a 19-year-old fine arts student at the march near Cairo University, where security forces had parked two tanks and blocked the main road with barbed wire.

"I'm against Morsi but I'm not for people killing others and I'm not for the military government we have now," said Madkour, a female protestor in Cairo.

Some students dismissed those views.

"Al-Sisi is a hero and there's no one like him," said Rania Ibrahim, 18. "Morsi was a traitor and the Brotherhood are dogs!" her friend added.

Small protests also occurred at Helwan University in southern Cairo, witnesses said. At Zagazig University, northeast of Cairo, pro-Brotherhood students clashed with residents and Brotherhood opponents with fists, sticks and stones, security sources said. Eight people were wounded.

Army chief General Abdel Fattah al-Sisi, whom the now-banned Muslim Brotherhood accuses of staging a coup, kept Egyptians guessing about his political ambitions, declining to confirm or deny whether he would run for president.

"I think the time is not suitable now to ask this question while the country is passing through challenges and dangers that require us to be focused," he said in an interview on the website of the al-Masry al-Youm daily.