In this work, we present the development and application of a convolutional neural network (CNN)-based algorithm to precisely determine the interaction position ofγ-quanta in large monolithic scintillators. Those are used as an absorber component of a Compton camera (CC) system under development for ion beam range verification via prompt-gamma imaging. We examined two scintillation crystals: LaBr3:Ce and CeBr3. Each crystal had dimensions of 50.8 mm × 50.8 mm × 30 mm and was coupled to a 64-fold segmented multi-anode photomultiplier tube (PMT) with an 8 × 8 pixel arrangement. We determined the spatial resolution for three photon energies of 662, 1.17 and 1.33 MeV obtained from 2D detector scans with tightly collimated137Cs and60Co photon sources. With the new algorithm we achieved a spatial resolution for the CeBr3 crystal below 1.11(8) mm and below 0.98(7) mm for the LaBr3:Ce detector for all investigated energies between 662 keV and 1.33 MeV. We thereby improved the performance by more than a factor of 2.5 compared to the previously used categorical average pattern algorithm, which is a variation of the well-established k-nearest neighbor algorithm. The trained CNN has a low memory footprint and enables the reconstruction of up to 104events per second with only one GPU. Those improvements are crucial on the way to future clinicalin vivoapplicability of the CC for ion beam range verification.