The differences in size and function between primate and rodent brains, and the association of disturbed excitatory/inhibitory balance with many neurodevelopmental disorders highlight the importance to study primate ganglionic eminences (GEs) development. Here we used single-cell RNA and ATAC sequencing to characterize the emergence of cell diversity in monkey and human GEs where most striatal and cortical interneurons are generated. We identified regional and temporal diversity among progenitor cells which give rise to a variety of interneurons. These cells are specified within the primate GEs by well conserved gene regulatory networks, similar to those identified in mice. However, we detected, in human, several novel regulatory pathways or factors involved in the specification and migration of interneurons. Importantly, comparison of progenitors between our human and published mouse GE datasets led to the discovery and confirmation of outer radial glial cells in GEs in human cortex. Our findings reveal both evolutionarily conservative and nonconservative regulatory networks in primate GEs, which may contribute to their larger brain sizes and more complex neural networks compared with mouse.