The statement says 28 “terrorists” have been killed in the fighting, seven civilians and 10 members of Tunisia’s security forces.
In Paris, France’s foreign ministry identified the gunmen as “coming from Libyan territory”. But Tunisian Prime Minister Habib Essid directly accused Islamic State, also known as ISIS or ISIL.
While the situation has calmed down, authorities said a curfew will be implemented in the city on Monday evening.
The IS also claimed responsibility for the June and November attacks.
Ben Gardane is a major border town near Libya, and has been accused of being a hub for arms smuggling by militants around the border.
Bodies of dead insurgents lay in the streets said residents.
“I see three corpses on the ground”, she said.
The AP quoted a witness who said the gunmen spoke of creating a caliphate and “liberating” the town.
Speaking from Tunis, Nicholas Noe, of MideastWire.com, said the latest attack is a “significant turn” for Tunisia and the regional security.
The militants – thought to have swarmed over from the Libyan side of the border – fought running battles with police and soldiers in the town of Ben Guerdan, not far from the tourist resort of Djerba.
Washington has said Chouchane was likely among the dozens of militants killed, and that the strike probably averted a mass shooting or similar attack in Tunisia.
Islamic State fighters are now estimated to number between 2,000 and 5,000 in several different cells across Libya.
“This is an unprecedented attack, planned and organized”.
The predawn firefight at Ben Guerdane, Tunisia, 18 miles from the border, killed 21 attackers, with six more captured.
Tunisian security forces killed at least 35 militants in a series of failed attacks on multiple border posts Monday morning.
Last week, Tunisian security forces killed five heavily-armed men in an hours-long gunfight after they crossed into the country from Libya with a larger group.
State Department spokesman John Kirby condemned the “cowardly attack” and offered fresh U.S. help to Tunis, while European Union foreign policy chief Federica Mogherini said the attack “once more demonstrates the gravity of the threat faced by Tunisia“.
Monday’s attack came weeks after a US airstrike killed almost 40 people at an Islamic State training camp in the Libyan city of Sabratha, near the Tunisian border.
A medic said a 12-year-old boy was among the dead. The interior ministry said at least four of the five militants were Tunisians who had entered from Libya in a bid to carry out attacks in their homeland.
Turmoil followed in other countries such as Libya and Egypt that were also caught up in what was called the Arab Spring, while protests in Syria spiraled into a bloody civil war that still rages today.