The low-temperature magnetic properties of polycrystalline Na₂IrO₃, a candidate material for the realization of a quantum spin-liquid state, were investigated by means of muon-spin relaxation and nuclear magnetic resonance methods under chemical and hydrostatic pressure. The Li-for-Na chemical substitution promotes an inhomogeneous magnetic order, whereas hydrostatic pressure (up to 3.9 GPa) results in an enhancement of the ordering temperature T_N. In the first case, the inhomogeneous magnetic order suggests either short- or long-range correlations of broadly distributed j = ½ Ir⁴⁺ magnetic moments, reflecting local disorder. The increase of T_N under applied pressure points at an increased strength of three-dimensional interactions arising from interlayer compression.