CAIRO (Reuters) - An attack with a rocket propelled grenade killed two policemen and wounded another in the capital of Egypt's restive North Sinai province, state media reported late on Thursday.

The policemen were in their patrol car in Al-Arish when a rocket propelled grenade struck the vehicle, state media said. There was no immediate claim of responsibility.

It was the third attack in the Egyptian capital in recent weeks.

On Tuesday night, a homemade bomb exploded near the Supreme Court in downtown Cairo, injuring 12 people.

Last month, a bomb blast near the Egyptian foreign ministry killed three policemen in the worst attack in central Cairo for months. Islamist militant group Ajnad Misr claimed that attack.

Security forces are struggling to quell an Islamist insurgency that has killed scores of soldiers and policemen in the peninsula, which borders Israel and the Palestinian Gaza Strip.

The attacks surged after the military overthrew Islamist President Mohamed Mursi last year and the militants extended their reach to the Egyptian mainland with a series of bombings.

(Reporting by Mostafa Hashem; Writing by Shadi Bushra; Editing by Cynthia Osterman and David Gregorio)