British interior minister Theresa May, and her French and German counterparts, visited the site of the attack near the Imperial Marhaba hotel in the resort town of Sousse, laying flowers on the beach. They promised Tunisia help in security, intelligence, police training and to help keep tourism alive.
Tourism Police, armed with handguns and rifles, patrolled the waterfront where some European tourists remained amid the parasols and bouquets scattered in the sand.
Interior Minister Najem Gharsalli gave no details of those arrested and said officials were checking whether gunman Saif Rezgui had been trained in neighboring Libya in jihadist camps.
Forensic evidence shows Rezgui, a student who gave few clues to family and friends that he had been radicalized, was probably the only gunman, though others may have been involved in planning and organizing the attack.
"We will find all those involved, whether it was just logistical support or not," the Tunisian minister said, flanked by ministers from Britain, France and Germany.
Lone gunman?
Tunisia, which had a relatively peaceful transition to democracy after its 2011 "Arab Spring" uprising, has one of the most secular state structures in the Arab world. But it is also struggling with a rise in Islamist militancy.
Islamist jihadists have hit North African tourist sites before in Tunisia and Morocco, seeing them as legitimate targets because of their open Western lifestyles, free mixing of the sexes and tolerance of alcohol.
The number of Britons confirmed killed by the Islamist gunman in Friday's attack has risen to 18 from 15 and the final death toll of Britons is likely to increase to around 30 people, a British spokeswoman said.
British police are in Tunisia helping in the process of formally identifying victims.
"What happened here last Friday was a despicable act of cruelty," British minister May told reporters. "How could a place of such beauty, of relaxation, be turned into a scene of brutality and destruction?
"We have discussed concrete ways in which we can share our expertise in which we can help each other in dealing with this terrible threat we all face."
French Interior Minister Bernard Cazeneuve said cooperation could include intelligence-sharing and coordination with frontier police and airport security.
Tour companies have helped thousands of tourists leave Tunisia since Friday's attack on a country that relies heavily on tourism for jobs and foreign currency revenues.
Rezgui, the gunman, dressed in shorts and a T-shirt, opened fire with a rifle he had hidden in an umbrella at British, German, Belgian and Irish tourists as they lounged at the beach and pool.
The attack came three months after two gunmen killed 21 people at the Bardo Museum in Tunis. Both had spent time with Tunisian jihadists training in neighboring Libya.
"There is a large possibility that he was in Libya for about a month this year for training," said a security source with knowledge of the investigation. "We are still confirming that."
In turmoil amid a conflict between two rival governments, Libya has increasingly become a haven for Islamist militant groups who have profited from the chaos to seek shelter.
More than 3,000 Tunisians have left to fight for Islamist militant groups in Syria and Iraq, and increasingly in Libya, where some have set up training camps for jihadis or taken a leading role in Islamic State ranks there.
Watch: Eyewitness account: 'I turned around and the gunman was next to me'
