CAIRO, Egypt - The head of Egypt's Coptic Orthodox Church appealed to the government on Monday to address Christians complaints about discrimination to ease tensions as fierce riots broke out in the capital following a New Year's Day church bombing that killed 21 people.

The interview with Coptic Pope Shenouda III on state television came as hundreds of predominantly Christian protesters clashed with riot police in northern Cairo in late night demonstrations expressing frustration with the government's policies.

In rare criticism by the 87-year-old church leader, Shenouda called on the government to address Christian grievances in the country, especially of laws restricting freedom of worship.

"The state also has a duty. It must see to the problems of the Copts and try to resolve them," he said. "If there are laws that is an unjust to some, the state should correct many laws.

The pope said the unprecedented attack on the Saints Church in Alexandria had "caused panic" among Muslims and Christians, but he appealed for calm among his flock and warned that political activists might use protests to push their anti-government agenda.

"Problems are solved with calm and communication, not with anger and emotions," he said, while acknowledging that the tensions were fed by the Christian community's long-standing grievances.

"There are laws that are painful to some, and despite our commitment to the laws, the pain is still there, and this needs to be addressed," he said, while counselling patience to Christians.

The bombing touched off three days of protests involving clashes with both security forces and Muslim passers-by in the area around the church in Alexandria.

The community, which makes up 10 per cent of Egypt's 80 million, complains bitterly of discrimination in building its churches and in the job market and also feels the government is not confronting rising conservative Islamic prejudice in society.

In northern district of Shubra, police surrounded hundreds of protesters in tight cordons near the neighbourhood's main church, while youths dashed out of sidestreets and pelted their armoured cars with rocks.

Riot police beat the protesters with their batons and an Associated Press photographer on the scene saw at least five people injured including two bleeding from serious head wounds. A priest eventually convinced security forces to open their lines and allow the protesters to disperse.

Protesters also attempted to block a nearby highway with burning tires and threw rocks at passing cars.

In Alexandria, the police cordoned off the area around the church that was attacked to prevent further protests and enforce calm. Church supporters prevented a local construction company from repairing the damage to the building because parishioners want to keep the blood of the dead on the walls as a reminder, said a local priest.

"They don't want to erase the blood of martyrs," said Father Mena of the Saints Church.

Investigators, meanwhile, said they are focusing on a set of unidentified remains, including a severed head, from the bomb attack that may be linked to the attacker, a security official said.

Typically in suicide bombings, the head of the attacker is flung away by the blast but remains in one piece and police are now trying to reconstruct the face, said the official, speaking on condition of anonymity because he was not authorized to speak to the press.

No group has claimed responsibility for the attack, the worst on Egyptian Christians in a decade, but security officials now say police are looking at homegrown Islamic extremists perhaps were inspired by al-Qaida.

The crime lab investigation found the explosives used were locally made using TNT explosives and were filled with nails and ball bearings to maximize the number of casualties.