No one has claimed responsibility for the assault, in which eight troops were initially reported killed.
The official says three more slain soldiers were found on Friday morning outside the restive city of el-Arish. In Thursday night’s attack, a suicide car bomber and dozens of heavily armed militants stormed a checkpoint manned by some 30 troops. At least 12 troops were reported wounded.
The official spoke on condition of anonymity because he wasn’t authorized to speak to the media.
Egypt’s Islamic State affiliate is active in Sinai, where the Egyptian army is fighting to curb a militant insurgency and consolidate its grip on the area.