Mula Mustafe Bašeskije runs from Vječna Vatra to Baščaršija Square.
It is presumed that, even in Roman times, a road was in use here, and during the Ottoman period it was divided into three separate streets: Ćemaluša, Za Banjom and Varoš.
The section between the hamam and Gazi Husrev-Begova St. was called Za Banjom or Sokak Gazi Husrev-Begov Hamam. The rest of the street that ran to Baščaršija Square was called Varoš or Gornja Varoš. This part of town was a largely Orthodox Christian neighborhood.
With the onset of Austro-Hungarian rule, the street that ran from Baščaršija to Ali Pasha’s Mosque was called Ćemaluša. After the Sarajevo Assassination, from 1914 to 1919, the section that ran between Vječna Vatra and Cathedral was called Vojvotkinje Sofije and the part that stretched from Cathedral to Baščaršija was given the name, Potjorekova St.
After 1919, the long stretch between Baščaršija and Marijin Dvor was named after the crown prince, and later king, Aleksandar Karađorđević.
From 1941 to 1945 it was named after the head of the NDH, Ante Pavelić, and then in 1945 it was called Maršala Tita St.
In 1993 it was divided into two sections. The western section retained the name, Titova, and the eastern extent was named after the writer, Mula Mustafa Ševki Bašeskija (1731–1808). His “Ljetopis” (Chronicles) serves as a valuable source of information about Sarajevo from the second half of the 18th century.