Annotating lots of 3D medical images for training segmentation models is time-consuming.The goal of weakly supervised semantic segmentation is to train segmentation models without using any ground truth segmentation masks. Our work addresses the case where only image-level categorical labels, indicating the presence or absence of a particular region of interest (such as tumours or lesions), are available.Most existing methods rely on class activation mapping (CAM). We propose a novel approach, ToNNO, which is based on the Tomographic reconstruction of a Neural Network's Output. Our technique extracts stacks of slices with different angles from the input 3D volume, feeds these slices to a 2D encoder, and applies the inverse Radon transform in order to reconstruct a 3D heatmap of the encoder’s predictions. This generic method allows to perform dense prediction tasks on 3D volumes using any 2D image encoder. We apply it to weakly supervised medical image segmentation by training the 2D encoder to output high values for slices containing the regions of interest. We test it on four large scale medical image datasets and outperform 2D CAM methods. We also propose to combine tomographic reconstruction with CAM methods in order to obtain even better results.