The French anti-terrorist prosecutor has opened an investigation into the deadly shooting attack at the Ghriba synagogue on Tunisia's Djerba island that left five people dead, including a Franco-Tunisian man.

The Paris-based National anti-terrorist prosecutor (Pnat) said that it was opening an investigation into Tuesday's attack because of one of the victim's French nationality. It said it was assigning the investigation to the DGSI intelligence agency.

Benjamin Haddad, 42, had made the annual pilgrimage to the Ghriba synagogue with his cousin Aviel, and both were shot when the gunman, a member of the Tunisian National Guard, opened fire in front.

He was shot and killed by police officers, three of whom died in the attack.

Criminal or terrorist investigation?

Tunisian authorities have opened a preliminary criminal investigation into what Tunisian President Kais Saied called a "criminal and cowardly" attack.

Haddad came from a very religious Jewish family in the southern French city of Marseilles, according to Roland Elbez, political advisor to the president of the Marseille Jewish community, Michel Cohen-Tenoudji.

A father of four, Haddad ran a kosher bakery in the centre of the city.

(with wires)