In this study, we investigated whether multipotent (human-bone-marrow-derived mesenchymal stem cells [hBM-MSCs]) and pluripotent stem cells (murine-induced pluripotent stem cells [iPSCs] and murine embryonic stem cells [ESCs]) respond to nanocomposite fibrous mats of poly(L-lactic acid) (PLLA) loaded with 1 or 8 wt % of calcium-deficient nanohydroxyapatite (d-HAp). Remarkably, the dispersion of different amounts of d-HAp to PLLA produced a set of materials (PLLA/d-HAp) with similar architectures and tunable mechanical properties. After 3 weeks of culture in the absence of soluble osteogenic factors, we observed the expression of osteogenic markers, including the deposition of bone matrix proteins, in multi/pluripotent cells only grown on PLLA/d-HAp nanocomposites, whereas the osteogenic differentiation was absent on stem-cell-neat PLLA cultures. Interestingly, this phenomenon was confined only in hBM-MSCs, murine iPSCs, and ESCs grown on direct contact with the PLLA/d-HAp mats. Altogether, these results indicate that the osteogenic differentiation effect of these electrospun PLLA/d-HAp nanocomposites was independent of the stem cell type and highlight the direct interaction of stem cell-polymeric nanocomposite and the mechanical properties acquired by the PLLA/d-HAp nanocomposites as key steps for the differentiation process.