In March 2020, the SARS-CoV-2 virus outbreak was declared as a world pandemic by the World Health Organization (WHO). The only measures for controlling the outbreak are testing and isolation of infected cases. Molecular real-time polymerase chain reaction (PCR) assays are very sensitive but require highly equipped laboratories and well-trained personnel. In this study, a rapid point-of-need detection method was developed to detect the RNA-dependent RNA polymerase (RdRP), envelope protein (E), and nucleocapsid protein (N) genes of SARS-CoV-2 based on the reverse transcription recombinase polymerase amplification (RT-RPA) assay. RdRP, E, and N RT-RPA assays required approximately 15 min to amplify 2, 15, and 15 RNA molecules of molecular standard/reaction, respectively. RdRP and E RT-RPA assays detected SARS-CoV-1 and 2 genomic RNA, whereas the N RT-RPA assay identified only SARS-CoV-2 RNA. All established assays did not cross-react with nucleic acids of other respiratory pathogens. The RT-RPA assay's clinical sensitivity and specificity in comparison to real-time RT-PCR (n = 36) were 94 and 100% for RdRP; 65 and 77% for E; and 83 and 94% for the N RT-RPA assay. The assays were deployed to the field, where the RdRP RT-RPA assays confirmed to produce the most accurate results in three different laboratories in Africa (n = 89). The RPA assays were run in a mobile suitcase laboratory to facilitate the deployment at point of need. The assays can contribute to speed up the control measures as well as assist in the detection of COVID-19 cases in low-resource settings.