The attacks come after several days ago a militant group warned that it had planted explosives near the presidential palace in the capital.
According to the Egyptian Interior Ministry, a colonel was killed and several policemen injured on Monday when a bomb they were trying to defuse exploded.
Later as policemen cordoned off the area and tried to defuse another explosive, it went off killing a lieutenant colonel. Several officers were also wounded in the incident.
It was not clear whether President Abdel Fattah al-Sisi was in the Ittihadiya Palace when the explosions took place.
On Wednesday, five small bombs exploded in the Cairo metro stations, injuring five people, while two people were killed when two bombs went off on Saturday in a telecommunication tower.
Egypt has been struck by a wave of violence since the ouster of Mohammad Morsi, in July 2013 in a military coup led by Sisi, the then commander-in-chief of the Egyptian army.Smoke billows moments after a bomb blast in the vicinity of the Ittihadiya palace in the Egyptian capital Cairo, on June 30, 2014.