Rift Valley Fever Virus (RVFV) is a veterinary and human pathogen and is an agent of bioterrorism concern. Currently, RVFV treatment is limited to supportive care, so new drugs to control RVFV infection are urgently needed. RVFV is a member of the Bunyavirales order, and replication of these viruses depends on the viral endonuclease activity of the viral L protein. Screening for RVFV replication inhibitors among compounds with divalent cation-coordinating motifs similar to known viral nuclease inhibitors identified 31 novel RVFV inhibitors with selective indexes from 5 – 402 and 50% effective concentrations of 0.54 – 56 µM in Vero cells, primarily α-Hydroxytropolones and N-Hydroxypyridinediones. Inhibitor activity and selective index was validated in the human cell line A549. To evaluate specificity, select compounds were tested against another Bunyavirus, La Crosse Virus (LACV). Conservation of the enzymatic activity such as the cap-snatching mechanism among the Bunyavirales implies that the α-Hydroxytropolone and N-Hydroxypyridinedione chemotypes hold potential for development into treatments for related pathogens, including Hantaan Virus, Severe fever with thrombocytopenia syndrome virus, Crimean-Congo Hemorrhagic Fever Virus, and LACV. Keywords: Rift Valley Fever Virus 1, La Crosse virus 2, Cap-snatching endonuclease 3, Replication inhibitors 4, α-Hydroxytropolones 5, N-Hydroxypyridinediones 6.