The sources told AFP that two brothers of the Khachnaoui family, their sister and father were arrested Wednesday night in Kasserine near the border with Algeria, where the family has a small farm.
Prime Minister Habib Essid, hours after Wednesday's attack, identified one of the two attackers killed as Hatem Khachnaoui.
But police sources in his home village of Ibrahim Zahar, southwest Tunisia, said his first name was in fact Jabeur.
Yesterday, the presidency announced the arrests of "four people directly linked to the (terrorist) operation and five suspected of having ties to the cell".
The Islamic State group has claimed responsibility for the attack.