The Tazy or Kazakh National sighthound has been officially recognized as the national heritage of Kazakhstan. Comprehensive genetic studies of genetic diversity and population structure that could be used for selection and conservation of this unique dog breed have not been conducted so far. The aim of this study was to determine the genetic structure of the Tazy using microsatellite and SNP markers and to place the breed in the context of the world sighthound breeds. Our results showed that all 19 microsatellite loci examined were polymorphic. The observed number of alleles in the Tazy population varied from 6 (INU030 locus) to 12 (AHT137, REN169D01, AHTh260, AHT121, and FH2054 loci) with a mean of 9.778 alleles per locus. The mean number of effective alleles was 4.869 and ranged from 3.349 f to 4.841. All markers were highly informative (PIC values greater than 0.5) and ranged from 0.543 (REN247M23 locus) to 0.865 (AHT121 locus). The observed and expected heterozygosities in a total population were 0.748 and 0.769 and ranged from 0.746 to 0.750 and 0.656 to 0.769, respectively. Overall, the results confirmed that the Tazy breed has a high level of genetic diversity, no significant inbreeding, and a specific genetic structure. Three gene pools underlie the genetic diversity of the Tazy breed. SNP analysis using the CanineHD SNP array, which contains more than 170,000 SNP markers, showed that the Tazy breed is distinct from other sighthound breeds and genetically related to ancient eastern sighthound breeds sharing the same branch with the Afghan Hound and the Saluki. The results, together with archeological findings, confirm the ancient origin of the breed. The findings can be used for the conservation and international registration of the Tazy dog breed.