In this article, we comprehensively evaluate the vulnerability of state-of-the-art face recognition systems to template inversion attacks using 3D face reconstruction. We propose a new method (called GaFaR) to reconstruct 3D faces from facial templates using a pretrained geometry-aware face generation network, and train a mapping from facial templates to the intermediate latent space of the face generator network. We train our mapping with a semi-supervised approach using real and synthetic face images. For real face images, we use a generative adversarial network (GAN)-based framework to learn the distribution of generator intermediate latent space. For synthetic face images, we directly learn the mapping from facial templates to the generator intermediate latent code. Furthermore, to improve the success attack rate, we use two optimization methods on the camera parameters of the GNeRF model. We propose our method in the whitebox and blackbox attacks against face recognition systems and compare the transferability of our attack with state-of-the-art methods across other face recognition systems on the MOBIO and LFW datasets. We also perform practical presentation attacks on face recognition systems using the digital screen replay and printed photographs, and evaluate the vulnerability of face recognition systems to different template inversion attacks.