In this work, two different laterites (iron contents of 13.07 and 49.34 wt%, respectively, for lateritic clay, LAC, and iron-rich laterite, LAI) were selected and calcined at 600 °C. The obtained calcined laterites, namely LAI600 and LAC600, were separately mixed with an alkaline solution (silicate modulus of 1.35) or an acidic solution (phosphoric acid solution at pH ≤ 2) for the synthesis of inorganic polymer products. The fabricated products were cured at 20 °C (ambient) and 40 °C (oven). The obtained results showed that the compressive strength of each series of alkaline-based inorganic polymer binder increased with ageing time (7 and 28 days) for room temperature curing, while the reverse trend was noted for oven-cured specimens. The best mechanical performance was obtained when using a phosphoric acid solution, 38 and 52 ± 1 MPa; 62 and 65 ± 1 MPa at 28 days for LAC and LAI respectively. It appeared that a higher iron content within the laterite contributed to an increase in the compressive strength under acidic conditions (LAI (59 MPa) > LAC (48 MPa)) compared to the behavior obtained under alkaline conditions (LAI (6 MPa) < LAC (29 MPa)). Accordingly, the acidic products exhibited a dense structure (with lower porosity) and contained amorphous iron/aluminium phosphate phases such as berlinite (FePO4), iron hydrogen phosphate hydrate (Fe3H15(PO4)8·4H2O), ferrowyllieite (AlFe2Na2(PO4)3) and sodium iron phosphate (Na3Fe2(PO4)3) arising from the alteration of iron minerals in an acidic medium, confirmed by Mössbauer spectroscopy and electron paramagnetic resonance spectroscopy.