We present a new interpretation of the Kolárovo gravity and magnetic anomalies in the Danube Basin based on an inversion methodology that comprises the following numerical procedures: removal of regional trend, depth-wise separation of signal of sources, approximation of multiple sources by 3D line segments, non-linear inversion based on local corrections resulting in found sources specified as 3D star-convex homogenous bodies and/or 3D contrasting structural contact surfaces. This inversion methodology produces several admissible solutions from the viewpoint of potential field data. These solutions are then studied in terms of their feasibility taking into consideration all available tectono-geological information. By this inversion methodology we interpret here the Kolárovo gravity and magnetic anomalies jointly. Our inversion generates several admissible solutions in terms of the shape, size and location of a basic intrusion into the upper crust, or the shape and depth of the upper/lower crust interface, or an intrusion into the crystalline crust above a rise of the mafic lower crust. Our intrusive bodies lie at depths between 5 and 12 km. Our lower crust elevation rises to 12 km with and 8 km without the accompanying intrusion into the upper crust, respectively. Our solutions are in reasonable agreement with various previous interpretations of the Kolárovo anomaly, but yield a better and more realistic geometrical resolution for the source bodies. These admissible solutions are next discussed in the context of geological and tectonic considerations, mainly in relation to the fault systems.