Protein-arginine N-methyltransferase that catalyzes both the monomethylation and asymmetric dimethylation of the guanidino nitrogens of arginine residues in target proteins, and therefore falls into the group of type I methyltransferases (By similarity). May regulate retinoic acid synthesis and signaling by inhibiting ALDH1A1 retinal dehydrogenase activity (By similarity). L-arginyl-[protein] + S-adenosyl-L-methionine = H(+) + N(omega)-methyl-L-arginyl-[protein] + S-adenosyl-L-homocysteine L-arginyl-[protein] + 2 S-adenosyl-L-methionine = 2 H(+) + N(omega),N(omega)-dimethyl-L-arginyl-[protein] + 2 S-adenosyl-L-homocysteine Inhibited by N-ethylmaleimide and high concentrations of zinc chloride. Monomer and homodimer (By similarity). Interacts with EPB41L3 (via FERM domain); the interaction is direct and inhibits the protein-arginine N-methyltransferase activity of PRMT3. Interacts with the 40S ribosomal protein RPS2. Interacts with ALDH1A1; the interaction is direct, inhibits ALDH1A1 aldehyde dehydrogenase activity and is independent of the methyltransferase activity of PRMT3 (By similarity). The C2H2-type zinc-finger is responsible for substrate specificity. Belongs to the class I-like SAM-binding methyltransferase superfamily. Protein arginine N-methyltransferase family.