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 (PubMed:22795084, PubMed:23445220, PubMed:25728001, PubMed:31378783, PubMed:33495566, PubMed:39513743). Catalyzes the asymmetric arginine dimethylation at multiple sites in the Arg/Gly-rich region of small ribosomal subunit protein uS5/RPS2 (PubMed:22795084). Also appears to methylate other ribosomal proteins (By similarity). May regulate retinoic acid synthesis and signaling by inhibiting ALDH1A1 retinal dehydrogenase activity (PubMed:33495566). Contributes to methylation of histone H4 'Arg-3', a specific tag for epigenetic transcriptional activation (PubMed:25728001, PubMed:31378783, PubMed:39513743). Mediates asymmetric arginine dimethylation of histone H4 'Arg-3' (H4R3me2a) in the promoter region of miRNA miR-3648, to promote its transcription and osteogenesis (PubMed:31378783). {ECO:0000250|UniProtKB:Q922H1, ECO:0000269|PubMed:22795084, ECO:0000269|PubMed:23445220, ECO:0000269|PubMed:25728001, ECO:0000269|PubMed:31378783, ECO:0000269|PubMed:33495566, ECO:0000269|PubMed:39513743}. This is the function of PRMT3 (protein arginine methyltransferase 3, ENSG00000185238).