Analysts said Monday's attacks show that jihadists are keen to spread their influence from Libya to Tunisia and to set up a new stronghold in the country.
Prime Minister Habib Essid said about 50 extremists were believed to have taken part in the coordinated dawn attacks on an army barracks and police and National Guard posts in the border town of Ben Guerdane.
He said that 36 attackers had been killed and seven captured in a fierce firefight that also saw the deaths of seven civilians and 12 security force personnel.
He said three civilians and 14 security personnel were also wounded.
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"The (security forces') reaction was rapid and strong. We won a battle and are prepared for any others," Essid said.
"Now they know Tunisia is no easy pushover and that it is not so simple to set up an emirate in Ben Guerdane."
Yesterday, Essid said that the operation's aim had been to create a "Daesh (IS) emirate" in the town.
Michael Ayari, an analyst with the International Crisis Group, agreed, saying the attacks were an "extension of the armed conflict so far confined to Libya".