In statements broadcast on state television, Essebsi said the assault that killed 28 jihadists was "maybe aimed at controlling" the border region with Libya, and vowed to "exterminate these rats".
The attacks in the border town of Ben Guerdane, where 10 members of the security forces and seven civilians also lost their lives, were "unprecedented" and coordinated", said the president.
"Maybe they were aimed at controlling this region" in order to proclaim a "new (jihadist) province", he said.
Tunisian forces fought off today's assailants in the second day of clashes in the border area in less than a week.
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Tunisia has seen an emergence of radical Islam since the 2011 uprising that toppled longtime autocratic strongman Zine El Abidine Ben Ali who suppressed opponents including Islamists.
In recent years a large number of Tunisians have joined the Islamic State group (IS) in Libya, where authorities say they have been trained to carry out attacks at home.
Last year IS -- which has set up an Islamic "caliphate" in parts of Syria and Iraq under its control and is also active in Egypt -- claimed three attacks in Tunisia, killing dozens of foreign tourists and presidential guards.