Although atrial fibrillation (AF) is the most common sustained atrial arrhythmia, treatment success for this condition remains suboptimal. Information from magnetic resonance imaging (MRI) has the potential to improve treatment efficacy, but there are currently few automatic tools for the segmentation of the atria in MR images. In the study, we propose a LA-Net, a multi-task network optimised to simultaneously generate left atrial segmentation and edge masks from MRI. LA-Net includes cross attention modules (CAMs) and enhanced decoder modules (EDMs) to purposefully select the most meaningful edge information for segmentation and smoothly incorporate it into segmentation masks at multiple-scales. We evaluate the performance of LA-Net on two MR sequences: late gadolinium enhanced (LGE) atrial MRI and atrial short axis balanced steady state free precession (bSSFP) MRI. LA-Net gives Hausdorff distances of 12.43 mm and Dice scores of 0.92 on the LGE (STACOM 2018) dataset and Hausdorff distances of 17.41 mm and Dice scores of 0.90 on the bSSFP (in-house) dataset without any post-processing, surpassing previously proposed segmentation networks, including U-Net and SEGANet. Our method allows automatic extraction of information about the LA from MR images, which can play an important role in the management of AF patients.