The influenza A virus (IAV) RNA polymerase (FluPol) primes the viral transcription by using capped 5 prime-ends snatched from host nascent RNAs. However, the exact localization of the FluPol on the genome or the timing of its snatching activity remains poorly characterized. Here, we have monitored IAV infection from the perspective of the FluPol interaction with the host chromatin template. Quantification of chromatin-bound RNAs shows a significant perturbation in host transcription that correlates with a relocalization of RNA polymerase II (RNAPII) from the gene bodies to downstream intergenic regions. This extended transcription leading to the production of RNA downstream of genes (DoGs) was previously linked to the NS1-mediated inhibition of the transcriptional termination. However, immunoprecipitation of FluPol-bound RNA in the chromatin fraction revealed that FluPol remains linked to nascent host transcripts during phases of transcriptional elongation and termination, thereby extending the window of opportunity in which cap-snatching may occur. In addition, chromatin-associated FluPol was enriched at transcription termination sites, suggesting that it may participate in the virus-induced termination defects. Finally, we observed that, rather than targeting just highly expressed genes, the FluPol was preferentially recruited to promoters activated by the viral infection and enhancers. Together, these observations suggest the FluPol uses the early immune response to target regulatory elements of defense-related genes at which it interferes with the fate of the transcripts, and possibly also limits RNAPII re-initiation by impairing the termination process.