Automated interpretation of seismic images using deep learning methods is challenging because of the limited availability of training data. Few-shot learning is a suitable learning paradigm in such scenarios due to its ability to adapt to a new task with limited supervision (small training budget). Existing few-shot semantic segmentation (FSSS) methods fix the number of target classes. Therefore, they do not support joint training on multiple datasets varying in the number of classes. In the context of the interpretation of seismic facies, fixing the number of target classes inhibits the generalization capability of a model trained on one facies dataset to another, which is likely to have a different number of facies. To address this shortcoming, we propose a few-shot semantic segmentation method for interpreting seismic facies that can adapt to the varying number of facies across the dataset, dubbed the AdaSemSeg. In general, the backbone network of FSSS methods is initialized with the statistics learned from the ImageNet dataset for better performance. The lack of such a huge annotated dataset for seismic images motivates using a self-supervised algorithm on seismic datasets to initialize the backbone network. We have trained the AdaSemSeg on three public seismic facies datasets with different numbers of facies and evaluated the proposed method on multiple metrics. The performance of the AdaSemSeg on unseen datasets (not used in training) is better than the prototype-based few-shot method and baselines.