The early diagnosis of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections is required to identify and isolate contagious patients to prevent further transmission of SARS-CoV-2. In this study, we present a multitarget real-time TaqMan reverse transcription PCR (rRT-PCR) assay for the quantitative detection of SARS-CoV-2 and some of its circulating variants harboring mutations that give the virus a selective advantage. Seven different primer-probe sets that included probes containing locked nucleic acid (LNA) nucleotides were designed to amplify specific wild-type and mutant sequences in Orf1ab, Envelope (E), Spike (S), and Nucleocapsid (N) genes. Furthermore, a newly developed primer-probe set targeted human β2-microglobulin (B2M) as a highly sensitive internal control for RT efficacy. All singleplex and fourplex assays detected £ 14 copies/reaction of quantified synthetic RNA transcripts, with a linear amplification range of nine logarithmic orders. Primer-probe sets for detection of SARS-CoV-2 exhibited no false-positive amplifications with other common respiratory pathogens, including human coronaviruses NL63, 229E, OC43, and HKU-1. Fourplex assays were evaluated using 160 clinical samples positive for SARS-CoV-2. Results showed that SARS-CoV-2 viral RNA was detected in all samples, including viral strains harboring mutations in the Spike coding sequence that became dominant in the pandemic. Given the emergence of SARS-CoV-2 variants and their rapid spread in some populations, fourplex rRT-PCR assay containing four primer-probe sets represents a reliable approach to allow quicker detection of circulating relevant variants in a single reaction.