We have investigated the magnetic and optical properties of chemically low temperature-synthesized Zn_1–xFe_xO (x=0.05 and 0.10) diluted magnetic semiconducting nanoparticles (~7 nm). Observed magnetic behaviour of x=0.05 samples showed that the net magnetic interaction was antiferromagnetic-like, a feature established by Curie–Weiss fit, concave Arrott–Belov–Kouvel (ABK) plots with the absence of spontaneous magnetization even at 5K and stretched exponential-type time-dependent magnetization behaviour. Optimization of the Fe(x) dopant concentration in Zn1–xFexO gave the most favourable roomtemperature ferromagnetism for x=0.10, as supported by finite coercive field (~94.4 Oe) and remanent magnetization (0.011 m_B/Fe ion) from strong hysteretic magnetization vs. magnetic-field curves at room temperature. The Curie temperature of the x=0.10 sample was estimated at ~388 K. The existence of a room-temperature ferromagnetic phase was further established by the convex nature of the ABK plots with finite spontaneous magnetization. The observed magnetic behaviour for different x values is best explained by a magnetic polaron model.