A subform of peroxisome that corresponds to an intermediate in a peroxisome assembly pathway, which operates by conversion of peroxisomal subforms in the direction P1, P2 -> P3 -> P4 -> P5 -> P6. P3 peroxisomes are formed by fusion of P1 and P2 peroxisomes, and are distinguished from the other subforms on the bases of buoyant density and protein content.