Fully convolutional neural networks (FCNNs) trained on a large number of images with strong pixel-level annotations have become the new state of the art for the semantic segmentation task. While there have been recent attempts to learn FCNNs from image-level weak annotations , they need additional constraints, such as the size of an object, to obtain reasonable performance. To address this issue, we present motion-CNN (M-CNN), a novel FCNN framework which incorporates motion cues and is learned from video-level weak annotations. Our learning scheme to train the network uses motion segments as soft constraints, thereby handling noisy motion information. When trained on weakly-annotated videos, our method outperforms the state-of-the-art EM-Adapt approach on the PASCAL VOC 2012 image segmentation benchmark. We also demonstrate that the performance of M-CNN learned with 150 weak video annotations is on par with state-of-the-art weakly-supervised methods trained with thousands of images. Finally, M-CNN substantially outperforms recent approaches in a related task of video co-localization on the YouTube-Objects dataset. This is an extended version of our ECCV 2016 paper.