CAIRO, Oct 18 (Reuters) - Thousands of supporters of Egypt's deposed President Mohamed Mursi protested in Cairo on Friday, shouting slogans against army chief General Abdel Fattah al-Sisi, who removed him on July 3.

One person was injured by gunfire when taking part in a pro-Mursi march of a few thousand in Fayoum, south of Cairo, state news agency MENA reported. Four were injured in clashes between Mursi-supporters and residents in the Nile Delta city of Zagazig, state TV reported.

Hundreds of pro-Mursi Islamists took to the streets in the coastal city of Alexandria and in Buhayra province, witnesses and security sources said.

Friday's protests remained mostly peaceful. On Oct. 6, dozens of supporters of Mursi's Muslim Brotherhood were killed in protests in one of the bloodiest days since the military deposed him.

Interior minister Mohamed Ibrahim, who survived an assassination attempt in September, ordered police to confront decisively any attempt to break the law, MENA reported.

On Aug. 14, Egyptian security forces broke up two pro-Mursi sit-ins in Cairo and killed hundreds of civilians.

The government then declared a state of emergency and imposed a curfew. Thousands of Brotherhood members, including Mursi himself, have been arrested.

Gunmen killed a policeman on Friday on a street in the city of El-Arish in north Sinai, security and medical sources said.

Egypt is fighting an Islamist insurgency in the largely lawless Sinai Peninsula, adjoining the Palestinian Gaza strip and Israel. Sinai-based militants have intensified their attacks on military and police since July. (Reporting by Shadia Nasralla and Ali Abdelatti; editing by Andrew Roche)