The replication and pathogenicity of influenza A virus (FLUAV) are controlled in part by the alpha/beta interferon (IFN-α/β) system. This virus-host interplay is dependent on the production of IFN-α/β and on the capacity of the viral nonstructural protein NS1 to counteract the IFN system. Two different mechanisms have been described for NS1, namely, blocking the activation of IFN regulatory factor 3 (IRF3) and blocking posttranscriptional processing of cellular mRNAs. Here we directly compare the abilities of NS1 gene products from three different human FLUAV (H1N1) strains to counteract the antiviral host response. We found that A/PR/8/34 NS1 has a strong capacity to inhibit IRF3 and activation of the IFN-β promoter but is unable to suppress expression of other cellular genes. In contrast, the NS1 proteins of A/Tx/36/91 and of A/BM/1/18, the virus that caused the Spanish influenza pandemic, caused suppression of additional cellular gene expression. Thus, these NS1 proteins prevented the establishment of an IFN-induced antiviral state, allowing virus replication even in the presence of IFN. Interestingly, the block in gene expression was dependent on a newly described NS1 domain that is important for interaction with the cleavage and polyadenylation specificity factor (CPSF) component of the cellular pre-mRNA processing machinery but is not functional in A/PR/8/34 NS1. We identified the Phe-103 and Met-106 residues in NS1 as being critical for CPSF binding, together with the previously described C-terminal binding domain. Our results demonstrate the capacity of FLUAV NS1 to suppress the antiviral host defense at multiple levels and the existence of strain-specific differences that may modulate virus pathogenicity.