1. Modelling approaches aimed at identifying currently unknown hosts of zoonotic diseases have the potential to make high-impact contributions to global strategies for zoonotic risk surveillance. However, geographical and taxonomic biases in host-pathogen associations might influence reliability of models and their predictions. 2. Here we propose a methodological framework to mitigate the effect of biases in host–pathogen data and account for uncertainty in models’ predictions. Our approach involves identifying “pseudo-negative” species and integrating sampling biases into the modelling pipeline. We present an application on the Betacoronavirus genus and provide estimates of mammal-borne betacoronavirus hazard at the global scale. 3. We show that the inclusion of pseudo-negatives in the analysis improves the overall performance of our model significantly (AUC = 0.82 and PR-AUC = 0.48, on average) compared to a model that does not use pseudo-negatives (AUC = 0.75 and PR-AUC = 0.39, on average), reducing the rate of false positives. Results of our application unveil currently unrecognised hotspots of betacoronavirus hazard in subequatorial Africa, and South America. 4. Our approach addresses crucial limitations in host–virus association modelling, with important downstream implications for zoonotic risk assessments. The proposed framework is adaptable to different multi-host disease systems and may be used to identify surveillance priorities as well as knowledge gaps in zoonotic pathogens’ host-range.