Data distillation and coresets have emerged as popular approaches to generate a smaller representative set of samples for downstream learning tasks to handle large-scale datasets. At the same time, machine learning is being increasingly applied to decision-making processes at a societal level, making it imperative for modelers to address inherent biases towards subgroups present in the data. While current approaches focus on creating fair synthetic representative samples by optimizing local properties relative to the original samples, their impact on downstream learning processes has yet to be explored. In this work, we present fair Wasserstein coresets (FWC), a novel coreset approach which generates fair synthetic representative samples along with sample-level weights to be used in downstream learning tasks. FWC uses an efficient majority minimization algorithm to minimize the Wasserstein distance between the original dataset and the weighted synthetic samples while enforcing demographic parity. We show that an unconstrained version of FWC is equivalent to Lloyd's algorithm for k-medians and k-means clustering. Experiments conducted on both synthetic and real datasets show that FWC: (i) achieves a competitive fairness-utility tradeoff in downstream models compared to existing approaches, (ii) improves downstream fairness when added to the existing training data and (iii) can be used to reduce biases in predictions from large language models (GPT-3.5 and GPT-4).