Catalyzes the two successive C-2 and C-7 methylation reactions involved in the conversion of uroporphyrinogen III to precorrin-2 via the intermediate formation of precorrin-1. It is a step in the biosynthesis of both cobalamin (vitamin B12) and siroheme. 2 S-adenosyl-L-methionine + uroporphyrinogen III = H(+) + precorrin-2 + 2 S-adenosyl-L-homocysteine Cofactor biosynthesis; adenosylcobalamin biosynthesis; precorrin-2 from uroporphyrinogen III: step 1/1. Porphyrin-containing compound metabolism; siroheme biosynthesis; precorrin-2 from uroporphyrinogen III: step 1/1. Belongs to the precorrin methyltransferase family.