A blast took place in front of Cairo's Cancer Institute building earlier in August, killing 22 people and injuring 47 others.
Security investigations revealed the elements had planned to plant an explosive device in one of Giza's streets, the statement read.
Four individuals, believed to be belonging to the terrorist movement Hasm, were arrested last week. They admitted amid investigation that they had received military and technical training on the manufacture of explosives.
A military court adjourned the trial of 304 defendants over attempting to assassinate Assistant General Prosecutor Zakaria Abdel Aziz to July 9.
Supreme State Security ordered holding in custody 14 members of "Hasm Movement", an offshoot of the terrorist Muslim Brotherhood for 15 days pending investigations.
Egyptian security forces have arrested and killed dozens of suspected Hasm members in the past few months.
Three Hasm terrorists were killed while exchanging fire with security forces, stated the Ministry of Interior on Monday.
Two terrorists from Hasm movement were killed in a shoot-out with security forces in Qalyoubia governorate
Police officers killed a “terrorist” during a gunfight and chase on Oasis road in Giza on Friday.