Catalyzes the tetrapolymerization of the monopyrrole porphobilinogen (PBG) into the hydroxymethylbilane pre-uroporphyrinogen in several discrete steps. H2O + 4 porphobilinogen = hydroxymethylbilane + 4 NH4(+) Binds 1 dipyrromethane group covalently. Porphyrin-containing compound metabolism; protoporphyrin-IX biosynthesis; coproporphyrinogen-III from 5-aminolevulinate: step 2/4. The porphobilinogen subunits are added to the dipyrromethane group. Present with 8480 molecules/cell in log phase SD medium. Belongs to the HMBS family.