A machine learning approach was applied to geochemical analysis of nine obsidian blades discovered in the archaeological site of Tulūl al-Baqarat (4th millennium BCE, Iraq), aiming at unraveling the provenance of the natural material (volcanic glass, obsidian) employed for carving the studied tools. To accomplish this, we measured the geochemical composition of each archaeological tool to characterize the material, using non-invasive and non-destructive techniques. The obtained data were compared with other compositional data from obsidian sources in volcanic districts of the Near East in terms of major, minor, and trace elements. Significantly useful were the Zr and Rb minor elements, which have a remarkable discriminatory capacity in large volcanic contexts. To obtain more detailed discrimination, we also applied principal component analysis (PCA: covariate matrix) modeling and automatically compared these compositional data via a machine learning approach. Obsidian tools from Tulūl al-Baqarat show a rhyolitic composition and a geochemical fingerprint that allowed to exclude most obsidian outcrops in Turkish and Armenian volcanic sites as original sources, due to the different abundances of minor elements and PCA results. The most interesting outcome of our study indicates that obsidian blades resulted geochemically comparable to volcanic glasses from Nemrut Dağ stratovolcano (Southeastern Turkey), in accordance with the results (averaged probability) obtained via a machine learning approach. The possible provenance from Nemrut Dağ stratovolcano is remarkable because it is located on the Turkish route of the Tigris River, providing supporting evidence of a trade network and broad exchange activity since the 4th millennium BCE from Turkey and the south Near East to the shores of the Persian Gulf.