The official stressed the "absence of incriminating evidence at this stage." He spoke on condition of anonymity to discuss an ongoing investigation.
Four men and a woman close to the attacker have been in custody since Tuesday.
French and Tunisian authorities say they have not confirmed any links between the attacker and the Islamic State group or radical Islam. A counterterrorism probe has been opened, but the attacker's motive remains unclear. He was shot dead after the attack on Sunday.
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