Type I interferons (IFN) help clear a viral infection, but IFN levels can then decline to reset the antiviral state and avoid innate immune dysregulation. Such dysregulation can occur following infection with highly pathogenic and pandemic RNA viruses, such as H5N1 influenza A viruses or SARS-CoV-2. In spite of the strong innate immune response that these viruses induce, pandemic viruses replicate and spread successfully, suggesting that they can circumvent the effects of IFN. Innate immune activation is triggered when host cells detect viral RNA, especially defective viral genomes (DVGs). A strong IFN response (e.g. to DVGs or a highly immunogenic wild-type infection) must then decline through negative feedback involving the IFN receptor. How DVGs modulate this feedback remains poorly understood. To quantify positive and negative IFN regulation, we first performed in vitro experiments combining different doses of viral RNA and exogenous IFN, and measured subsequent IFN expression. We next developed an in vivo Bayesian computational model that captures the impact of influenza virus DVGs on both positive and negative IFN feedback. Competition between DVGs and virus is also considered. Finally, we calibrated this model on published in vitro and in vivo influenza virus infection data. Our model suggests that the cumulative IFN exposure of a host cell, rather than the instantaneous IFN level, shapes further IFN induction; this gives DVGs a dual role: beyond triggering IFN induction, they can also lower it through negative feedback. Our model further predicts that these effects are important locally, shaping the spatial dynamics of the response, allowing suppression of innate immune responses in neighbouring, uninfected cells. Through this model, we can explain two important biological observations: i) IFN levels can decline while virus and DVG levels continue to rise in tissue culture and mouse infections; and ii) pandemic viruses that produce high levels of immunogenic RNA molecules can successfully replicate through local innate immune suppression. Overall, we propose that heterogeneity within viral populations (including DVGs and other noncanonical viral RNAs) can modulate positive and negative feedback loops and shape infection outcomes. More broadly, our work may support studies into the therapeutic use of these viral RNA populations. Author summary: Humans and animals have to fight influenza virus and other infections without inducing immunopathology. After detection of an infection, the innate immune system produces type I interferon (IFN), a signal that starts a protective response. However, high levels of IFN and prolonged IFN expression can cause damage to tissues and worsen disease. Negative feedback is one route by which IFN production can stop, but its activation during viral infection remains poorly understood. A central question is why viruses can continue to replicate and spread despite a strong IFN response. We here investigated why IFN levels can begin to decline while virus levels continue to rise during influenza virus infection. This decline is most pronounced when the virus produces large amounts of defective viral genomes (DVGs). These defective genomes arise naturally during viral replication and are produced by many RNA viruses, including SARS-CoV-2, Ebola virus, and measles virus. Using cell-culture experiments, computational modelling, and fitting of our model to cell-culture and mouse data, we find that defective genomes contribute to both IFN activation and its negative feedback. Both the experiments and model support a mechanism in which IFN accumulation during infection suppresses its own production, and that this suppression can start earlier under strong DVG stimulation. At the local level, this can allow viral spread to continue even while overall IFN levels remain high. Overall, our findings reveal an additional level of interplay between defective viral genomes and the host innate immune system. They also suggest that the potential therapeutic use of defective genomes must be carefully calibrated to achieve an optimal antiviral response.