Eight people, including a woman, remain in Tunisian police custody on suspicion of being directly linked to the deadly attack on tourists in Sousse, a minister has announced.
Four other people who had been detained have been released, he added.
Thirty-eight tourists were killed when gunman Sefeddine Rezgui opened fire on a beach.
ISIS militant group has claimed responsibility for the attack.
Thirty of the victims were British citizens.
Tunisia’s government fears the attack will destroy its tourism industry, the country’s biggest foreign currency earner.
Government minister Kamel Jendoubi said at a media conference that investigations had “allowed us to discover the network behind the operation in Sousse”.
Kamel Jendoubi did not elaborate on the identities of the suspects or their alleged role.
He said ten UK investigators were assisting with the investigation, the AFP news agency reports.
Kamel Jendoubi also said that Tunisia has deployed 1,377 armed security agents at hotels and on beaches to guarantee the safety of people, AFP reports.
Tunisian authorities have identified 23-year-old student Seifeddine Rezgui as the gunman who carried out the attack.
Police have released photos of two suspects, Bin Abdallah and Rafkhe Talari – friends of Seifeddine Rezgui whom they are yet to locate.
Tunisian officials believe both the Sousse and Bardo museum gunmen were trained in Libya, which has been mostly lawless since NATO-led forces overthrew long-serving ruler Muammar Gaddafi in 2011.
ISIS has built a significant presence in Libya, Tunisia’s eastern neighbor, and is thought to control the major towns of Derna and Sirte.