Rift Valley Fever phlebovirus (RVFV), genus Phlebovirus, family Phenuiviridae, order Bunyavirales, has a single-stranded, negative-sense RNA genome, consisting of L, M and S segments. Here, we report the establishment of a strand-specific, quantitative reverse transcription (RT)-PCR assay system that can selectively distinguish between the genomic and antigenomic RNAs of each of the three viral RNA segments produced in RVFV-infected cells. To circumvent the obstacle of primer-independent cDNA synthesis during RT, we used a tagged, strand-specific RT primer, carrying a non-viral 'tag' sequence at the 5' end, which ensured the strand-specificity through the selective amplification of only the tagged cDNA in the real-time PCR assay. We used this assay system to examine the kinetics of intracellular accumulation of genomic and antigenomic viral RNAs in mammalian cells infected with the MP-12 strain of RVFV. The genomic RNA copy numbers, for all three viral RNA segments, were higher than that of their corresponding antigenomic RNAs throughout the time-course of infection, with a notable exception, wherein the M segment genomic and antigenomic RNAs exhibited similar copy numbers at specific times post-infection. Overall, this assay system could be a useful tool to gain an insight into the mechanisms of RNA replication and packaging in RVFV.