Superconducting properties of 19-filament multi-core MgB₂ wires reinforced by stainless steel sheath were investigated by magnetic measurements. The samples have filament diameters, ϕ, between 58 and 17 μm. No influence of ϕ on superconducting transition temperature is found, but width of transition increases with shrinking filament size. Whereas three of the four investigated samples show a systematic decrease of critical current density J _c with decreasing ϕ, the sample with largest filament diameter has a weaker field dependence leading to smaller values of J _c than for the sample with next largest ϕ at low fields but much higher values at high fields. This sample is also the only one showing clear anisotropy. Mean effective activation energies, U, are also reduced with ϕ, indicating a reduction of pinning strength. The temperature dependence of U points to the existence of activation energy distributions which broaden for samples with smaller filament diameter.