Mohamed Gharsalli said 1,000 troops would now be deployed to protect Tunisia’s beach resorts.
Three European ministers have laid flowers at the scene of the attack in a sign of solidarity.
Islamic State (ISIS) has said it was behind the attack.
“We have started by arresting a first group, a significant number of people, from the network that was behind this terrorist criminal,” said Mohamed Gharsalli, referring to Seifeddine Rezgui.
Tunisian authorities say Seifeddine Rezgui was the only attacker, but he had accomplices who provided him with weapons and logistical support, reports AP news agency.
“We are friends against one enemy,” said Mohamed Gharsalli, addressing his counterparts from the UK, Germany and France.
Seifeddine Rezgui came onto the beach from the sea either by jet ski or speedboat at about midday on June 26. He started shooting on the beach, entered the Hotel Imperial Marhaba and ran out of the front of the hotel before the police shot him dead.
The attack was the deadliest in Tunisia’s recent history. In March, militants killed 22 people, mainly foreigners, at the Bardo museum in the capital Tunis.
Tunisian authorities say army reservists will be deployed to tourist sites and that about 80 mosques accused of inciting violence will be closed within a week.
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