An Islamist militant group based in the Sinai Peninsula has claimed responsibility for Sunday's killing of a high ranking police officer in Cairo.

Ansar Bayt Al-Maqdis said the attack was in retaliation for the arrest of Islamist women and vowed to carry out more attacks until they are released.

Lieutenant-Colonel Mohamed Mabrouk was shot dead outside his home in Cairo's Nasr City district on Sunday. Security officials said he was in charge of the Muslim Brotherhood file at the interior ministry's national security agency. He had also been involved in drafting the charges against toppled Islamist president Mohamed Morsi and his Islamist movement.

Islamists have suffered a fierce crackdown by security forces since Morsi's ouster, with hundreds killed and thousands arrested, including top leaders of his Muslim Brotherhood movement.

"God helped the group kill the apostate, one of the biggest tyrants at state security, in response to the malicious arrest and investigation of free women," said the group's statement posted on a militant website.

On Monday, fifteen women and seven girls who support Morsi were referred to an urgent criminal court in Alexandria over clashes in the Mediterranean city. They are due appear in court on Wednesday.

The group called on its followers to help it find the interior ministry "tyrants" involved in arresting women. It threatened the interior ministry, the body responsible for the police, with a series of attacks until female detainees are released.

The Brotherhood has distanced itself from the attack, stressing it vehemently condemns the "heinous crime" against the officer.

Egypt's Sinai Peninsula, adjoining Israel and the Gaza Strip, has seen a sharp spike in militant attacks since the army, prompted by mass protests, deposed Morsi in July. Attacks in the capital have heightened fears that militant violence might take hold across the country.

In September, the same group, whose name means "Supporters of Jerusalem," claimed responsibility for a failed assassination attempt on the interior minister in Cairo.

Last year, the group claimed responsibility for almost a dozen attacks over two years on a gas pipeline linking Egypt, Israel and Jordan.