We quantify the role of Population ( Pop ) III core-collapse supernovae ( SNe ) as the first cosmic dust polluters . Starting from a homogeneous set of stellar progenitors with masses in the range [ 13 - 80 ] M _ { \odot } , we find that the mass and composition of newly formed dust depend on the mixing efficiency of the ejecta and the degree of fallback experienced during the explosion . For standard Pop III SNe , whose explosions are calibrated to reproduce the average elemental abundances of Galactic halo stars with [ Fe / H ] < -2.5 , between 0.18 and 3.1 M _ { \odot } ( 0.39 - 1.76 M _ { \odot } ) of dust can form in uniformly mixed ( unmixed ) ejecta , and the dominant grain species are silicates . We also investigate dust formation in the ejecta of faint Pop III SN , where the ejecta experience a strong fallback . By examining a set of models , tailored to minimize the scatter with the abundances of carbon-enhanced Galactic halo stars with [ Fe / H ] < -4 , we find that amorphous carbon is the only grain species that forms , with masses in the range 2.7 \times 10 ^ { -3 } - 0.27 M _ { \odot } ( 7.5 \times 10 ^ { -4 } - 0.11 M _ { \odot } ) for uniformly mixed ( unmixed ) ejecta models . Finally , for all the models we estimate the amount and composition of dust that survives the passage of the reverse shock , and find that , depending on circumstellar medium densities , between 3 and 50 % ( 10 - 80 % ) of dust produced by standard ( faint ) Pop III SNe can contribute to early dust enrichment .