Methylates arginine residues in proteins such as small nuclear ribonucleoproteins or histone H2A/H4. L-arginyl-[protein] + 2 S-adenosyl-L-methionine = 2 H(+) + N(omega),N(omega)'-dimethyl-L-arginyl-[protein] + 2 S-adenosyl-L-homocysteine Belongs to the class I-like SAM-binding methyltransferase superfamily. Protein arginine N-methyltransferase family.