Tardić was born in Šibenik, where he had a brother called Zorzi or Juraj. As a young man he was 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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