Security forces were still hunting for two men suspected of having trained in Libya with the gunman who killed 38 people, he added.
Most of the people killed on a beach in Sousse were from the UK, along with other European holidaymakers.
On Tuesday, police in Tunisia released photos of two men identified as Rafkhe Talari and Bin Abdallah, though their connection to the deceased gunman Seifeddine Rezgui was not clear.
Tunisia’s government fears the attack will destroy its tourism industry, the country’s biggest foreign currency earner.
Rafkhe Talari (left) and Bin Abdallah (right) are both wanted by Tunisian police Tunisia’s Radio Mosaique reported that Lazhar Akremi, minister for parliamentary relations, made the announcement at a party meeting late on Wednesday.
It was not immediately clear when all the arrests had been made.
In March, two gunmen killed 22 people at the famous Bardo museum in Tunisia’s capital, Tunis.
