"The gunmen were killed in a shootout with the guards of the governor of the Fayoum province," the source, requesting anonymity, told The Anadolu Agency.
Saturday's attack came one day after the governor's motorcade came under attack in the central province on Friday.
Egyptian authorities often blame the Muslim Brotherhood, the group from which ousted President Mohamed Morsi hails, for attacks against security forces and government officials.
The Brotherhood denies the accusations and says it is committed to peaceful activism.
Morsi, Egypt's first freely elected president, was ousted by the military in mid-2013 following massive protests against his administration.
Supporters of the ousted president describe his overthrow as a "military coup".