Premier Habib Essid also said that he believed most of the tourists killed in Friday's attack at the Imperial Marhaba Hotel in Sousse, a popular beach resort on Tunisia's Mediterranean coast, were British.
Tobias Ellwood, the junior foreign office minister of U.K., said Saturday that 15 British nationals were confirmed to be among the dead. Tunisian officials said that German, Belgian and Irish tourists were also among the 39 killed on Friday.
Hours after the massacre, the self-declared Islamic State claimed responsibility for the attack. The gunman, later killed by police, reportedly carried a Kalashnikov rifle concealed in a beach umbrella into the midst of sunbathers before opening fire.
Essid identified the assailant as Seifeddine Rezgui from the town of Gaafour in northern Tunisia, which is located about 85 miles northwest of the scene of Friday's attack. The Site Intelligence group, which monitors Islamist extremist activity, said the Islamic State had used a Twitter account to claim responsibility for the deadly attack, identifying the attacker by his jihadi pseudonym, Abu Yahya al-Qayrawani.
Sky News has a photo of what it claims to be him, dressed in a wetsuit and nonchalantly carrying an Kalashnikov by his side, immediately after the deadly rampage.
British Prime Minister David Cameron spoke of what he described as the "savage" attacks and vowed that "terrorists will not succeed." He said they were "a brutal and tragic reminder of the threat faced around the world from these evil terrorists." He said many of those killed in Tunisia were British.
The Guardian quotes Briton Tom Richards, a 22-year-old who was at the Tunisian beach resort along with this mother and brother at the time of the attack.
He said that hotel staff tried to lead them to safety inside the building, but the three were followed upstairs by the gunman who "shot two people, through the head" in front of them.
"Then Tom found himself face to face with the gunman, who was pointing a Kalashnikov assault rifle at him. 'He looked right at me — I thought I was dead,' said Tom. 'He was maybe 20 or 25, he had long black hair and a beard.'
"Then the gunman squeezed the trigger, and there was the shattering sound of bullets. The shots hit the marble floor, spraying Tom and his mother with shards of marble, wounding her in the ankle and catching Tom in the wrist."