Defects in nucleic acid metabolizing enzymes can lead to spontaneous but selective activation of either cGAS/STING or RIG-like receptor (RLR) signaling, causing type I interferon–driven inflammatory diseases. In these pathophysiological conditions, activation of the DNA sensor cGAS and IFN production are linked to spontaneous DNA damage. Physiological, or tonic, IFN signaling on the other hand is essential to functionally prime nucleic acid sensing pathways. Here, we show that low-level chronic DNA damage in mice lacking the Aicardi-Goutières syndrome gene SAMHD1 reduced tumor-free survival when crossed to a p53-deficient, but not to a DNA mismatch repair-deficient background. Increased DNA damage did not result in higher levels of type I interferon. Instead, we found that the chronic interferon response in SAMHD1-deficient mice was driven by the MDA5/MAVS pathway but required functional priming through the cGAS/STING pathway. Our work positions cGAS/STING upstream of tonic IFN signaling in Samhd1-deficient mice and highlights an important role of the pathway in physiological and pathophysiological innate immune priming.