A security source said the person killed was Bilel Kobi, an Algerian who was close to the network's leader Abdelmalek Droukdel.
Kobi had been charged with overseeing links between the network, known by its French initials AQMI, and its Tunisian branch, the official said on condition of anonymity.
Another Algerian, Bechir Bin Neji, thought to have been the commander of an AQMI cell in the Sammama region of Tunisia, was also found dead with an assault rifle by his side, Chibani said.
The Friday evening operation took place in the Mount Sammama area of central-western Tunisia, which lies in a range of hills that are a favoured hideout of Al-Qaeda and Islamic State group jihadists.
It is adjacent to Mount Chaambi, considered to be the jihadists' main rear base near the border with Algeria.
The area is the scene of regular clashes between the army and jihadist groups.
Tunisian authorities announced last spring that they had killed several members of AQMI's Tunisia branch, which had claimed a series of deadly attacks against security forces.
Since its 2011 revolution, Tunisia has faced a jihadist insurgency responsible for the deaths of dozens of soldiers, police, civilians and foreign tourists.
Tunisia has been under a state of emergency since November 2015, when a suicide bombing in Tunis claimed by the Islamic State jihadist group killed 12 presidential guards.
The last major attacks were a series of deadly operations in 2015 and an IS offensive into the town of Ben Guerdane on the Libyan border in March 2016.
Thousands of Tunisians have joined jihadist groups fighting in Iraq, Syria and neighbouring Libya.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)