"Eight people with direct links to the carrying out of the operation, including a woman, have been arrested," said Kamel Jendoubi, the minister who heads a crisis group set up after the attack.
"The security services have been able to... uncover and destroy the network that was behind this operation," Jendoubi told a news conference, without elaborating on their alleged role.
Jendoubi said British authorities were assisting with the investigation.
"As part of the security cooperation between Tunisia and Britain, 10 British investigators are working on the probe," he said.
Tunisia fears the attack -- which also claimed the lives of three people from Ireland, two from Germany and one each from Belgium, Portugal and Russia -- will damage its tourism industry.
The sector accounts for about seven percent of gross domestic product in a country already suffering from the upheaval that followed the 2011 overthrow of dictator Zine El Abidine Ben Ali.
- Fears for tourism -
After the attack -- which was claimed by the jihadist Islamic State group -- Tunisia's government pledged to boost security around hotels, beaches and attractions.
Jendoubi said 1,377 extra armed security officers had been deployed to reinforce police already on the ground.
But they were late to deploy in some tourist areas around Tunis and in the resort of Hammamet south of the capital, triggering the ire of Interior Minister Najem Gharsalli.
"We had agreed to protect the beaches. Where are the agents tasked with security the beaches," Gharsalli was heard telling a security official during an inspection of Hammamet.
"Where are they? Are they having a coffee," he added, according to a video posted on the website of private Cap FM radio Wednesday night.
An AFP correspondent who toured the beach resort of Gammarth northeast of Tunis on Thursday said there were still no security reinforcements around.
- Minute of remembrance -
Britain's Foreign Secretary Philip Hammond confirmed Tunisia's formal identification of 30 of those slain as Britons.
The bodies of eight were flown Wednesday to a Royal Air Force station north of London, in a solemn ceremony reminiscent of the repatriation of fallen soldiers.
The remains of nine others were flown out on Thursday and Hammond has said there would be other flights on Friday and Saturday.
"Tomorrow is also a week from the date of the attack, and we will be holding a minute's remembrance at noon across the UK as well as in British embassies and posts around the world."
Prime Minister David Cameron has promised to back a full investigation into the attack, calling for "a response at home and abroad" to violent Islamic fundamentalism.
Witnesses said the shooting rampage lasted more than 30 minutes before the gunman was shot dead, but officials say police were on the scene much sooner.
Sofiane Sliti, spokesman for the prosecutor, said investigators were on the scene one hour after the attack took place and examined all the bodies.
He said 18 were gunned down on the beach, while five bodies were found near the pool and the others elsewhere.
President Beji Caid Essebsi admitted security forces had not taken measures to protect beaches despite jihadist threats.
Friday's attack was the second on tourists in Tunisia claimed by IS in three months, after the extremist group said it was behind a March attack on the National Bardo Museum in Tunis that killed 22 people.
Tunisian authorities have said Rezgui received weapons training from jihadists in neighbouring Libya, travelling to the chaos-wracked country at the same time as the two young Tunisians behind the Bardo attack.
In the past four years, dozens of police and soldiers have been killed in Tunisia in clashes and ambushes attributed to jihadists -- mainly in the western Chaambi Mountains.
Disillusionment and social exclusion have fuelled radicalism among young Tunisians, with the country exporting some 3,000 jihadist fighters to Iraq, Syria and Libya.