The threat posed by coronaviruses to human health has necessitated the development of a highly specific and sensitive viral detection method that could differentiate between the currently circulating severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and other SARS-related coronaviruses (SARSr-CoVs). In this study, we developed a peptide nucleic acid (PNA)-based real-time quantitative polymerase chain reaction (RT-qPCR) assay targeting the N gene to efficiently discriminate SARS-CoV-2 from other SARSr-CoVs in human clinical samples. Without compromising the sensitivity, this method significantly enhanced the specificity of SARS-CoV-2 detection by 100-fold as compared to conventional RT-qPCR. In addition, we designed an RT-qPCR method for the sensitive and universal detection of ORF3ab-E genes of SARSr-CoV with a limit of detection (LOD) of 3.3 RNA copies per microliter. Thus, the developed assay serves as a confirmative dual-target detection method. Our PNA-mediated dual-target RT-qPCR assay can detect clinical SARS-CoV-2 samples in the range of 18.10–35.19 Ct values with an 82.6–100% detection rate. Furthermore, our assay showed no cross-reactions with other coronaviruses such as human coronaviruses (229E, NL63, and OC43) and Middle East respiratory syndrome coronavirus, influenza viruses (Type B, H1N1, H3N2, HPAI H5Nx, and H7N9), and other respiratory disease-causing viruses (MPV, RSV A, RSV B, PIV, AdV, and HRV). We, thus, developed a PNA-based RT-qPCR assay that differentiates emerging pathogens such as SARS-CoV-2 from closely related viruses such as SARSr-CoV and allows diagnosis of infections related to already identified or new coronavirus strains.