The emergence of novel SARS-CoV-2 genetic variants with increased transmissivity and reduced antibody neutralization efficiency is a threat to global public health. Reverse transcription polymerase chain reaction (RT-PCR) with the use of fluorescent probes, which make it possible to detect the single nucleotide substitutions, is a technique suitable for screening the SARS-CoV-2 RNA-containing samples for the already known functionally significant mutations in the S-gene, identification of which allows to define and differentiate the most epidemiologically significant genetic variants. The study was aimed to develop an assay for the large-scale monitoring of the spread of the SARS-CoV-2 top-priority variants. Based on the whole-genome alignment of the SARS-CoV-2 sequences, deposited in the GISAID database, primers and LNA-modified probes were selected to detect mutations in the S gene, typical for the Alpha, Beta/Gamma and Delta variants of concern (VOC). The developed reagent kit for detection of the key mutations in the SARS-CoV-2 S gene by the real time RT-PCR has good analytical and diagnostic characteristics and was authorized as a medical device (reagent) for in vitro use. The results of detecting the VOC and the key mutations with the use of the developed reagent kit were consistent with the data of the whole genome sequencing of 1,500 SARS-CoV-2 RNA samples. The developed reagent kit and the subsequent SARS-CoV-2 RNA sequencing assay used to perform the epidemiological monitoring of SARS-CoV-2 variants made it possible to promptly report the emergence of the Delta genetic variant in Russia, and to trace the dynamic changes in the prevalence of Delta in Moscow Region in April–September 2021.