State news agency TAP cites Prime Minister Habib Essid as saying that Khaled Chaieb, also known as Abou Sakhr Lokman, was killed overnight in an operation in the Gafsa region near the Algerian border.
Chaieb is believed a prominent militant in al-Qaida's North African arm, and suspected of leading or helping lead the March 18 attack on the National Bardo Museum.
Twenty-two people, mainly foreigners, and two gunmen were killed in the attack.
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