Statistical optimization of performance determining factors is essential for the development of a cesium removal system from aqueous solutions. Therefore, factorial experimental design and multiple regression techniques were employed to assess the primary and interaction effects of the pH, initial concentration, and contact time in the cesium removal process using nanoscale zero-valent iron-zeolite (nZVI-Z) and nano-Fe/Cu-zeolite (nFe/Cu-Z) as an adsorbent. The optimum region of cesium removal was identified by constructing a contour plot. The study revealed that initial concentration was the most significant factor followed by contact time. The study also suggested that maximum cesium removal occurred at pH, initial concentration, and contact time of 6, 200 mg/L, and 30 min, respectively. Moreover, the statistically significant interaction effect was observed between contact time and initial concentration. The experimental data were also fitted with Tόth, Langmuir, Dubinin-Astakhov (D-A), Freundlich, and Hill models and found that the Tόth model fitted better compared with the other four models based on Akaike information criterion (AIC) and root-mean-square deviation (RMSD). The findings of this paper can undoubtedly contribute to constructing the optimum statistical process of removing hazardous pollutants from the water, which significantly impacts on human health and the environment. Graphical abstract.