Ajnad Misr (Soldiers of Egypt) has claimed responsibility for an explosion near the foreign ministry that killed two police officers on Sunday.
The militant jihadist group published a statement on Twitter, saying the operation was part of their "Vengeance is Life" campaign against the police.
Revenge operations against "criminal organisations" will continue, the group said.
A bomb near the foreign ministry in downtown Cairo killed two lieutenant colonels on Sunday and left nine people injured.
The group had claimed responsibility for planting bombs near the Ittihadiya presidential palace on 30 June. The bombs killed two police officers and injured three people.
In May, the Islamist group was officially labeled a terrorist organisation.
Jihadist attacks on police and army personnel in the Sinai Peninsula and elsewhere in Egypt have left hundreds of soldiers and officers dead in the past year.
Ansar Bayt Al-Maqdis, a Sinai-based jihadist group, has claimed responsibility for most of the attacks.