Upon recognition of viral infections, the innate immune system triggers signal transduction pathways that induce the expression of mRNAs encoding antiviral factors, such as interferons (IFNs), IFN-stimulated genes (ISGs) and inflammatory cytokines. Regulation of cellular innate immune responses occurs at multiple levels, including nucleocytoplasmic trafficking of proteins and RNAs through the nuclear pore complex (NPC). Influenza A virus (IAV), like other RNA viruses, is susceptible to IFN-induced cellular responses. Consequently, IAV has developed multiple strategies to hijack the cellular machinery responsible for RNA and protein transport, thereby reducing host gene expression and suppressing antiviral responses. Here, we identified the tripartite motif containing 34 protein (TRIM34), an ISG member of the TRIM family, as a positive regulator of IAV replication in vitro. TRIM34 negatively modulates host gene expression and innate immune responses induced after viral infection in vitro and in vivo. Mechanistically, we show that TRIM34 interacts with nucleocytoplasmic transport factors, such as ribonucleic acid export 1 (RAE1) and nuclear pore complex protein 93 (Nup93), even in the absence of IAV infection. Remarkably, these TRIM34 interactions seem independent of TRIM34 E3 ubiquitin ligase activity, and affect the nuclear import of IFN-regulatory factor 3 (IRF3) and the nuclear export of host mRNAs encoding antiviral functions, without affecting the nuclear export of viral mRNAs, providing a likely mechanism by which TRIM34 dampens host innate immune responses. Such regulatory mechanisms are critical to avoid excessive or prolonged immune activation, which can be detrimental to the host. In addition, these TRIM34-mediated effects could be further exploited to develop new antiviral drugs against IAV and potentially other viral infections, as its activity is not restricted to IAV infections.