The reconstruction of the ventricular cardiac conduction system (CCS) from patient-specific data is a challenging problem. High-resolution imaging techniques have allowed only the segmentation of proximal sections of the CCS from images acquired ex vivo. In this paper, we present an algorithm to estimate the location of a set of Purkinje-myocardial junctions (PMJs) from electro-anatomical maps, as those acquired during radio-frequency ablation procedures. The method requires a mesh representing the myocardium with local activation time measurements on a subset of nodes. We calculate the backwards propagation of the electrical signal from the measurement points to all the points in the mesh to define a set of candidate PMJs that is iteratively refined. The algorithm has been tested on several Purkinje network configurations, with simulated activation maps, subject to different error amplitudes. The results show that the method is able to build a set of PMJs that explain the observed activation map for different synthetic CCS configurations. In the tests, the average error in the predicted activation time is below the amplitude of the error applied to the data.