The force of the blast destroyed the building which housed the military intelligence headquarters, leaving Egyptian soldiers and police trapped in the rubble, Israel Radio reported. At least 20 people were injured in the bombing, Ahram Online said.
Shortly after the incident, a second explosion occurred at a military checkpoint also near Rafah. Initial reports said a car bomb exploded at the checkpoint. There were no reports of casualties but clashes between soldiers and militants erupted, the radio said.
Ahram Online said the remains of two suicide bombers involved in the attacks were found.
Since the ouster of former president Mohamed Morsi on July 3, the Egyptian army has waged a crackdown on militant groups operating in the Sinai who have been responsible for attacks on Egyptian army and police positions, civilians and members of the clergy. More than 100 militants have been killed, Ahram Online said.