CAIRO, Sept 27 (Reuters) - Unidentified gunmen shot dead an Egyptian policeman on Friday in the city of El-Arish in North Sinai, near the border with the Palestinian Gaza Strip and Israel, state television reported.

The policeman was shot in the head, security sources said.

Attacks on the army and police have intensified since the military overtrew Egypt's first Islamist president, Mohamed Mursi, on July 3 after mass protests against his rule.

Since then, more than 100 members of the security forces have been killed in Sinai.

In Alexandria, dozens of people were hurt when pro-Mursi protesters clashed with residents, state TV reported.

Two explosive devices detonated near police check points on the outskirts of Cairo wounded two policemen, state news agency MENA said.

The army-installed government has mounted a campaign to crush Mursi's Muslim Brotherhood since his overthrow, killing hundreds of its supporters and arresting at least 2,000. A Cairo court on Monday banned the Brotherhood and ordered its funds seized.

(Reporting By Shadia Nasralla; Editing by Angus MacSwan)