The gunman who killed 38 at a beach near the Tunisian city of Sousse had help in carrying out the attack, officials say.
Interior ministry spokesman Mohamed Ali Aroui said authorities were “sure” that Seifeddine Rezgui had had accomplices.
The government has announced increased security measures after the attack claimed by Islamic State (IS).
On Sunday at least 30 of the dead were from the UK, the majority of those killed.
UK police say that 16 police officers have been deployed to Tunisia and hundreds more were working on the case in the UK in one of the largest counter-terrorism investigations since the 2005 London bombings.
Tunisian investigators believe the suspected accomplices provided the Kalashnikov assault rifle to Rezgui and helped him get to the scene, Mr Ali Aroui said.
He added that police were questioning Rezgui’s father and three roommates, although he did not say any of them were suspected of involvement in the attack.
Neighbours and relatives in Rezgui’s hometown of Gaafour have been telling journalists at their shock over his actions.
“Who could imagine he would commit such a horror?” uncle Ali Rezgui told Reuters.
“Maybe he was changed where he studied, maybe it was something on the internet. But we just don’t have any answers,” he added.
Tunisian authorities say army reservists will be deployed to tourist sites and that around 80 mosques accused of inciting violence will be closed within a week.
Friday’s 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.