A little-known Islamist militant group has claimed responsibility for a bombing in Egypt that killed a senior police officer.

Agnad Misr, or Soldiers of Egypt, which claims to have carried out eight attacks in Cairo since late 2013, said Wednesday's attack was in retaliation for the killing and arrest of Islamist supporters of deposed president Mohamed Morsi.

The car bomb killed Brigadier-General Ahmed Zaki outside his home in Sixth October City, an outer suburb of Cairo.

The group said it selected the time and place of the operation to ensure no "passersby were harmed."

The statement was carried late on Wednesday on a Facebook page under the group's name that has published previous statements. The page posted photos of a man alleged to be the slain officer on his way to a blue pick-up truck. Calling him a "criminal," the group said Zaki used the truck with no police identification because he feared being targeted.

In a video released last week, the group warned it would launch new attacks in revenge for abuses administered by the security forces.

Militant attacks targeting police and soldiers have become commonplace since the army ousted Islamist president Mohammed Morsi last summer amid millions-strong protests against his troubled rule. The government says approximately 500, mostly police and troops, have been killed.

Authorities have waged a harsh crackdown on Islamists, killing hundreds and jailing thousands of others since Morsi's removal.