Catalyzes the reductive methylation of deoxyuridylate to thymidylate. (6R)-5,10-methylene-5,6,7,8-tetrahydrofolate + dUMP = 7,8-dihydrofolate + dTMP Pyrimidine metabolism; dTTP biosynthesis. Homodimer. Belongs to the thymidylate synthase family.