Land cover classification is one of the most fundamental tasks in the field of remote sensing. In recent years, fully supervised fully convolutional network (FCN)-based semantic segmentation models have achieved state-of-the-art performance in the semantic segmentation task. However, creating pixel-level annotations is prohibitively expensive and laborious, especially when dealing with remote sensing images. Weakly supervised learning methods from weakly labeled annotations can overcome this difficulty to some extent and achieve impressive segmentation results, but results are limited in accuracy. Inspired by point supervision and the traditional segmentation method of seeded region growing (SRG) algorithm, a weakly towards strongly (WTS) supervised learning framework is proposed in this study for remote sensing land cover classification to handle the absence of well-labeled and abundant pixel-level annotations when using segmentation models. In this framework, only several points with true class labels are required as the training set, which are much less expensive to acquire compared with pixel-level annotations through field survey or visual interpretation using high-resolution images. Firstly, they are used to train a Support Vector Machine (SVM) classifier. Once fully trained, the SVM is used to generate the initial seeded pixel-level training set, in which only the pixels with high confidence are assigned with class labels whereas others are unlabeled. They are used to weakly train the segmentation model. Then, the seeded region growing module and fully connected Conditional Random Fields (CRFs) are used to iteratively update the seeded pixel-level training set for progressively increasing pixel-level supervision of the segmentation model. Sentinel-2 remote sensing images are used to validate the proposed framework, and SVM is selected for comparison. In addition, FROM-GLC10 global land cover map is used as training reference to directly train the segmentation model. Experimental results show that the proposed framework outperforms other methods and can be highly recommended for land cover classification tasks when the pixel-level labeled datasets are insufficient by using segmentation models.