Hydrological modelling can be complex in nonhomogeneous catchments with diverse geological, climatic, and topographic conditions. In this study, an integrated conceptual model including the snow module with machine learning modelling approaches was implemented for daily rainfall-runoff modelling in mostly karst Ljubljanica catchment, Slovenia, which has heterogeneous characteristics and is potentially exposed to extreme events that make the modelling process more challenging and crucial. In this regard, the conceptual model CemaNeige Génie Rural à 6 paramètres Journalier (CemaNeige GR6J) was combined with machine learning models, namely wavelet-based support vector regression (WSVR) and wavelet-based multivariate adaptive regression spline (WMARS) to enhance modelling performance. In this study, the performance of the models was comprehensively investigated, considering their ability to forecast daily extreme runoff. Although CemaNeige GR6J yielded a very good performance, it overestimated low flows. The WSVR and WMARS models yielded poorer performance than the conceptual and hybrid models. The hybrid model approach improved the performance of the machine learning models and the conceptual model by revealing the linkage between variables and runoff in the conceptual model, which provided more accurate results for extreme flows. Accordingly, the hybrid models improved the forecasting performance of the maximum flows up to 40 % and 61 %, and minimum flows up to 73 % and 72 % compared to the CemaNeige GR6J and stand-alone machine learning models. In this regard, the hybrid model approach can enhance the daily rainfall-runoff modelling performance in nonhomogeneous and karst catchments where the hydrological process can be more complicated.