Image stitching aim to align two images taken from different viewpoints into one seamless, wider image. However, when the 3D scene contains depth variations and the camera baseline is significant, noticeable parallax occurs-meaning the relative positions of scene elements differ substantially between views. Most existing stitching methods struggle to handle such images with large parallax effectively. To address this challenge, in this paper, we propose an image stitching solution called PIS3R that is robust to very large parallax based on the novel concept of deep 3D reconstruction. First, we apply visual geometry grounded transformer to two input images with very large parallax to obtain both intrinsic and extrinsic parameters, as well as the dense 3D scene reconstruction. Subsequently, we reproject reconstructed dense point cloud onto a designated reference view using the recovered camera parameters, achieving pixel-wise alignment and generating an initial stitched image. Finally, to further address potential artifacts such as holes or noise in the initial stitching, we propose a point-conditioned image diffusion module to obtain the refined result.Compared with existing methods, our solution is very large parallax tolerant and also provides results that fully preserve the geometric integrity of all pixels in the 3D photogrammetric context, enabling direct applicability to downstream 3D vision tasks such as SfM. Experimental results demonstrate that the proposed algorithm provides accurate stitching results for images with very large parallax, and outperforms the existing methods qualitatively and quantitatively.