The mechanism by which viral RNA-dependent RNA polymerases (RdRp) specifically amplify viral genomes is still unclear. In the case of flaviviruses, a model has been proposed that involves the recognition of an RNA element present at the viral 5' untranslated region, stem-loop A (SLA), that serves as a promoter for NS5 polymerase binding and activity. Here, we investigated requirements for specific promoter-dependent RNA synthesis of the dengue virus NS5 protein. Using mutated purified NS5 recombinant proteins and infectious viral RNAs, we analyzed the requirement of specific amino acids of the RdRp domain on polymerase activity and viral replication. A battery of 19 mutants was designed and analyzed. By measuring polymerase activity using nonspecific poly(rC) templates or specific viral RNA molecules, we identified four mutants with impaired polymerase activity. Viral full-length RNAs carrying these mutations were found to be unable to replicate in cell culture. Interestingly, one recombinant NS5 protein carrying the mutations K456A and K457A located in the F1 motif lacked RNA synthesis dependent on the SLA promoter but displayed high activity using a poly(rC) template. Promoter RNA binding of this NS5 mutant was unaffected while de novo RNA synthesis was abolished. Furthermore, the mutant maintained RNA elongation activity, indicating a role of the F1 region in promoter-dependent initiation. In addition, four NS5 mutants were selected to have polymerase activity in the recombinant protein but delayed or impaired virus replication when introduced into an infectious clone, suggesting a role of these amino acids in other functions of NS5. This work provides new molecular insights on the specific RNA synthesis activity of the dengue virus NS5 polymerase.