Antiviral agents are needed for the treatment of SARS-CoV-2 infections and to control other coronavirus outbreaks that may occur in the future. Here we report the identification and characterization of RNA-binding compounds that inhibit SARS-CoV-2 replication. The compounds were detected by screening a small library of antiviral compounds previously shown to bind HIV-1 or HCV RNA elements with a live-virus cellular assay detecting inhibition of SARS-CoV-2 replication. These experiments allowed detection of eight compounds with promising anti-SARS-CoV-2 activity in the sub-micromolar to micromolar range and wide selectivity indexes. Examination of the mechanism of action of three selected hit compounds excluded action on the entry or egress stages of the virus replication cycle and confirmed recognition by two of the molecules of conserved RNA elements of the SARS-CoV-2 genome, including the highly conserved S2m hairpin located in the 3'-untranslated region of the virus. While further studies are needed to clarify the mechanism of action responsible for antiviral activity, these results facilitate the discovery of RNA-targeted antivirals and provide new chemical scaffolds for developing therapeutic agents against coronaviruses.