The British Foreign Office, meanwhile, raised the death toll of British tourists killed in Friday's attack from 27 to 30.
Other European tourists were among the dead. The attack was Tunisia's deadliest ever and threatens to be a devastating blow to its tourism sector.
The Islamic State group claimed responsibility for the attack, in which Tunisian student Seifeddine Rezgui opened fire on a beach in the resort of Sousse. He was later killed by police.
He did not elaborate on their identities or roles, saying only that the investigation "has allowed us to discover the network behind the operation in Sousse."
The minister also urged greater international terrorism cooperation in a "war ... Between democratic Tunisia and an international jihadi movement."
Sofiane Selliki, an official in the prosecutor's office, said no one had been brought before a judge for charges. A top security official told the AP this week that Rezgui had trained in a jihadi camp in Libya at the same time as the two men who attacked a leading Tunisian museum in March, killing near.
More Tunisians -- about 3,000 -- are believed to have gone to Syria and Iraq to join radical jihadis including the Islamic State group than fighters from any other country.
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