Catalysis of the addition of a methyl group to either of the unmethylated terminal nitrogen atoms (also called omega nitrogen) in peptidyl-arginine to form an omega-N-G-monomethylated arginine residue. The reaction is S-adenosyl-L-methionine + -L-arginine = S-adenosyl-L-homocysteine + -Nomega-methyl-L-arginine.
protein arginine omega-N monomethylase activity