The optimisation of haematopoietic stem and progenitor cell expansion is on demand in modern cell therapy. In this work, haematopoietic stem/progenitor cells (HSPCs) have been selected from unmanipulated cord blood mononuclear cells (cbMNCs) due to adhesion to human adipose-tissue derived stromal cells (ASCs) under standard (20%) and tissue-related (5%) oxygen. ASCs efficiently maintained viability and supported further HSPC expansion at 20% and 5% O2. During co-culture with ASCs, a new floating population of differently committed HSPCs (HSPCs-1) grew. This suspension was enriched with СD34+ cells up to 6 (20% O2) and 8 (5% O2) times. Functional analysis of HSPCs-1 revealed cobble-stone area forming cells (CAFCs) and lineage-restricted colony-forming cells (CFCs). The number of CFCs was 1.6 times higher at tissue-related O2, than in standard cultivation (20% O2). This increase was related to a rise in the number of multipotent precursors - BFU-E, CFU-GEMM and CFU-GM. These changes were at least partly ensured by the increased concentration of MCP-1 and IL-8 at 5% O2. In summary, our data demonstrated that human ASCs enables the selection of functionally active HSPCs from unfractionated cbMNCs, the further expansion of which without exogenous cytokines provides enrichment with CD34+ cells. ASCs efficiently support the viability and proliferation of cord blood haematopoietic progenitors of different commitment at standard and tissue-related O2 levels at the expense of direct and paracrine cell-to-cell interactions.