Timely and affordable computer-aided diagnosis of retinal diseases is pivotal in precluding blindness. Accurate retinal vessel segmentation plays an important role in disease progression and diagnosis of such vision-threatening diseases. To this end, we propose a Multi-resolution Contextual Network (MRC-Net) that addresses these issues by extracting multi-scale features to learn contextual dependencies between semantically different features and using bi-directional recurrent learning to model former-latter and latter-former dependencies. Another key idea is training in adversarial settings for foreground segmentation improvement through optimization of the region-based scores. This novel strategy boosts the performance of the segmentation network in terms of the Dice score (and correspondingly Jaccard index) while keeping the number of trainable parameters comparatively low. We have evaluated our method on three benchmark datasets, including DRIVE, STARE, and CHASE, demonstrating its superior performance as compared with competitive approaches elsewhere in the literature.