Tardić was born in Šibenik, where he had a brother called Zorzi or Juraj. As a young man he was an enslaved as a prisoner of war and converted to Islam but under Gazi Husrev-beg he entered the Ottoman military, where he quickly rose through the ranks. As a close associate of Gazi Husrev-beg, he led numerous military conquests against the Croatian army in northern Bosnia and Croatia. In 1528, Murat-beg led the conquest of Jajce.
In 1536, Murad-beg Tardić was charged by Suleiman the Magnificent with 8,000 men to lay siege to the Klis Fortress under Petar Kružić. He was successful in the Siege of Klis, occupying it in 1537. For his military services he was put in charge of the Klis Sanjak with the title Beg. As the first Sanjak-Beg of Klis, he built a notable mosque in the town.
He was later made the beg of the Sanjak of Pojega in 1541 or in 1543. He is believed to have died in May 1545. He was buried in one of the two mausoleums (türbe) next to the Gazi Husrev-beg Mosque in Sarajevo.
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- Jurin Starčević, Kornelija (November 2006). "Islamic-Ottoman towns in the hinterland of Dalmatia: a contribution to the research of urban development in the 16th and the 17th centuries". Journal (Radovi) (in Croatian). Institute of Croatian History, Faculty of Philosophy, Zagreb. 38 (1): 126. ISSN 0353-295X. Retrieved 2012-07-02.
- Kužić, Krešimir (November 2005). "A Contribution to the Biographies of Some of Kačić's Knights and to the Origins of the Population of Their Territories". Radovi (in Croatian). Institute for Historical Sciences of the Croatian Academy of Sciences and Arts in Zadar (47): 218–219. ISSN 1330-0474. Retrieved 2012-07-02.