Influenza A virus and coronavirus strains cause a mild to severe respiratory disease that can result in death. Although vaccines exist against circulating influenza A viruses, such vaccines are ineffective against emerging pandemic influenza A viruses. Currently, no vaccine exists against coronavirus infections, including pandemic SARS-CoV-2, the causative agent of the Coronavirus Disease 2019 (COVID-19). To combat these RNA virus infections, alternative antiviral strategies are needed. A key drug target is the viral RNA polymerase, which is responsible for viral RNA synthesis. In January 2020, the World Health Organisation identified enisamium as a candidate therapeutic against SARS-CoV-2. Enisamium is an isonicotinic acid derivative that is an inhibitor of multiple influenza B and A virus strains in cell culture and clinically approved in 11 countries. Here we show using assays that enisamium and its putative metabolite, VR17-04, inhibit the activity of the influenza virus and the SARS-CoV-2 RNA polymerase. VR17-04 displays similar efficacy against the SARS-CoV-2 RNA polymerase as the nucleotide analogue remdesivir triphosphate. These results suggest that enisamium is a broad-spectrum small molecule inhibitor of RNA virus RNA synthesis, and implicate it as a possible therapeutic option for treating SARS-CoV-2 infection. Unlike remdesivir, enisamium does not require intravenous administration which may be advantageous for the development of COVID-19 treatments outside a hospital setting.