In single photon emission computed tomography (SPECT) with parallel hole collimation, image reconstruction is usually performed as a set of bidimensional (2D) analytical or iterative reconstructions. This approach ignores the tridimensional (3D) nature of scatter and detector response function that affects the detected signal. To deal with the 3D nature of the image formation process, iterative reconstruction can be used by considering a 3D projector modelling the 3D spread of photons. In this paper, we investigate the value of using accurate Monte Carlo simulations to determine the 3D projector used in a fully 3D Monte Carlo (F3DMC) reconstruction approach. Given the 3D projector modelling all physical effects affecting the imaging process, the reconstruction problem is solved using the maximum likelihood expectation maximization (MLEM) algorithm. To validate the concept, three data sets were simulated and F3DMC was compared with two other 3D reconstruction strategies using analytical corrections for attenuation, scatter and camera point spread function. Results suggest that F3DMC improves spatial resolution, relative and absolute quantitation and signal-to-noise ratio. The practical feasibility of the approach on real data sets is discussed.