The emergence of an RNA world requires among other processes the non-enzymatic, template-directed replication of genetic polymers such as RNA or related nucleic acids, possibly catalyzed by metal-ions. The absence of uridilate derivative polymerization on adenine containing templates has been the main issue preventing an efficient template-directed RNA polymerization. We report here the investigation of template-directed RNA polymerization in the eutectic phase in water-ice. In particular, it was found that activated uridilate monomers in the presence of metal-ion catalysts could efficiently elongate RNA hairpins whose 5'-overhangs served as the templating sequence. The same applies for every other pyrimidine and purine nucleobase. Moreover, the initial elongation rates were always higher in the presence of a template complementary to the nucleotide than in systems without proper base-pairing opportunities. These results suggest that a template-directed RNA polymerization catalyzed by metal-ions could be carried out under eutectic phase in water-ice conditions.