Eight suspects, including a woman, remain in custody on suspicion of being directly linked to last Friday's deadly attack on holidaymakers in the Tunisian resort of Sousse, a minister said Thursday, according to the BBC.
Four other people who had been detained have been released, he added.
The minister, Kamel Jendoubi, said at a media conference that investigations had "allowed us to discover the network behind the operation in Sousse''.
He did not elaborate on the identities of the suspects or their alleged role.
Jendoubi said 10 UK investigators were assisting with the investigation, and added that Tunisia has deployed 1,377 armed security agents at hotels and on beaches to guarantee the safety of the public.
38 tourists were killed in the attack, when a gunman opened fire on a beach. Islamic State (ISIS) has claimed responsibility for the attack.
Thirty of the victims were British, Foreign Secretary Philip Hammond has said.
Tunisian authorities have identified 28-year-old student Seifeddine Rezgui as the gunman who carried out the attack.
While authorities have said Rezgui acted alone during the attack, they believe he had accomplices who supported him beforehand.
Police have released photos of two suspects, Bin Abdallah and Rafkhe Talari - friends of Rezgui whom they are yet to locate, according to the BBC.
Officials believe both Rezgui and the terrorist who carried out an attack on a museum in March gunmen were trained in Libya.
British Prime Minister David Cameron said following the attack that ISIS terrorists are actively planning terrorist atrocities against the UK, and warned the group poses an existential threat to the western world.
The attack in Tunisia took place on the same day as a series of other attacks, at least one of which was also claimed by an ISIS-affiliate.
At least 27 people were killed in a suicide bombing at a Shiite mosque in Kuwait on the same day. The bomber is believed to have been a Saudi national, and a group linked to Islamic State claimed the attack shortly after.
Also on Friday, a Muslim terrorist beheaded his boss and injured several others in a gruesome attack in the French city of Lyon.
ISIS has encouraged its followers to carry out attacks during the Muslim holy month of Ramadan, though the State Department said after the three attacks that there was no evidence they were related.