By Maggie Fick

CAIRO (Reuters) - Hundreds of Muslim Brotherhood supporters chanted "Down with the military government" outside Cairo University on Tuesday, defying Egypt's army-backed authorities despite deadly clashes with security forces two days earlier.

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

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

The now-banned Muslim Brotherhood has accused the army, led by General Abdel Fatah al-Sisi, of staging a coup and working with security forces to eliminate the group through violence and arrests, allegations the military denies.

"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 Mursi but I'm not for people killing others and I'm not for the military government we have now," said Madkour, who wore a headscarf, as most Muslim women do in Egypt.

Some students dismissed those views.

"Sisi is a hero and there's no one like him," said Rania Ibrahim, 18. "Mursi 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, north east of Cairo, pro-Brotherhood students clashed with residents and Brotherhood opponents with fists, sticks and stones, security sources said. Eight people were wounded.

NGO REGISTRATION REVOKED

Authorities have cracked down on the Brotherhood in recent weeks. Security forces killed hundreds of pro-Mursi protesters in Cairo in August and then arrested many Brotherhood leaders.

On Tuesday, the government revoked the registration of a non-governmental organization set up by the Brotherhood in March to enable it to operate legally.

Last month, a court banned the Brotherhood and froze its assets, pushing the group, which had dominated elections held in Egypt after Mubarak's fall in 2011, further into the cold. A court is due to hear an appeal on October 22 against the decision.

The army has presented a political roadmap it promised would bring fair elections, but the Brotherhood has refused to take part in the transition, saying that would legitimize what it calls a military coup against an elected president.

Tamarud, the youth movement that had called for mass protests which pushed the army to depose Mursi, said in a statement it would to run in parliamentary elections, expected to take place early next year.

PROTECTING TOURIST SITES

Along with political turmoil, a surge in militant attacks has hurt tourism, a main foreign currency earner, due to fears it is no longer safe to visit Egypt's pyramids and beaches.

Hours after gunmen killed a police officer and wounded another in the Suez Canal city of Port Said on Tuesday, the interior ministry said Egypt may install security cameras at tourist sites to deter militants from targeting visitors.

"There's a security plan in place in tourist areas that will maintain stability in these areas," Interior Ministry spokesman Hany Abdel Latif said. "We expected all these problems because we are in a war against terrorism."

Al Qaeda-inspired militants have attacked police and soldiers almost daily in the Sinai Peninsula since Mursi fell.

The assaults are the most sustained since an Islamist insurgency that was crushed by then-President Hosni Mubarak in the 1990s, when militants killed tourists, government officials and policemen. A total of about 1,200 people died on both sides.

Attacks by militants in the Sinai have killed more than 100 soldiers and police since early July, the army said on September 15.

Last month the interior minister survived an assassination attempt in Cairo. Security and judicial sources said on Tuesday that three Egyptians linked to al Qaeda, and two Palestinians, were behind the attack. A Sinai-based Islamist militant group Ansar Bayt al-Maqdis had claimed responsibility for the failed attack.

Though the Brotherhood, which renounced violence decades ago, has been weakened, Islamist groups which sympathize with it show no signs of giving up protests against Mursi's overthrow.

With Egypt's oldest and best organized Islamist movement now effectively excluded from mainstream politics, the stage may be set for an insurgency to take hold beyond the Sinai, a stronghold for militants which is near the border with Israel.

On Monday, suspected militants killed six soldiers near the Suez Canal and fired rocket-propelled grenades at a state satellite station in Cairo.

The al-Furqan group claimed responsibility for the grenade attack in an Internet video whose authenticity could not be immediately verified.

(Additional reporting by Shadia Nasrallah; Writing by Michael Georgy and Yara Bayoumy; Editing by Alistair Lyon and Angus MacSwan)