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 order Bunyavirales, whose replication depends on the enzymatic activity of the viral L protein. Screening for RVFV inhibitors among compounds with divalent cation-coordinating motifs similar to known viral nuclease inhibitors identified 47 novel RVFV inhibitors with selective indexes from 1.1-103 and 50% effective concentrations of 1.2-56 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 a second Bunyavirus, La Crosse Virus (LACV), and the flavivirus Zika (ZIKV). These data indicate that the α-Hydroxytropolone and N-Hydroxypyridinedione chemotypes should be investigated in the future to determine their mechanism(s) of action allowing further development as therapeutics for RVFV and LACV, and these chemotypes should be evaluated for activity against related pathogens, including Hantaan virus, severe fever with thrombocytopenia syndrome virus, Crimean-Congo hemorrhagic fever virus.