CAIRO (Reuters) - At least three Egyptians were killed and eight wounded on Friday in separate incidents involving Islamist protesters and militants across the country, security and medical sources said.

Violence has polarised Egyptians since the army overthrew elected Islamist President Mohamed Mursi last year following mass protests against his rule.

Small hit-and-run demonstrations are the most Mursi's Muslim Brotherhood can muster after a fierce security crackdown in which hundreds have been killed and many thousands detained.

One civilian was killed and two others wounded by gunfire in northeast Cairo during clashes between Islamist protesters and residents, a security official said.

Further south in the province of Fayoum, a 17-year-old Islamist protester was killed during clashes with the police, medical and security sources said. Five others were wounded, including three policemen.

Security sources said another civilian was killed and one wounded when gunmen opened fire on an army checkpoint near the Suez Canal city of Ismailia.

The Brotherhood maintains it is a peaceful movement and denies involvement in anti-state violence that the government says has killed more than 500 people, mostly police and soldiers, since Mursi's ouster.

Attacks are often claimed by Islamist militants based mainly in the Sinai Peninsula, where the Egyptian army began clearing residents last week to create a buffer zone along the border with the Gaza Strip following attacks that killed 33 soldiers.

(Reporting by Mohamed Abdellah and Yusri Mohamed; Writing by Stephen Kalin; Editing by Tom Heneghan)