Existing communication methods for multi-agent reinforcement learning (MARL) in cooperative multi-robot problems are almost exclusively task-specific, training new communication strategies for each unique task. We address this inefficiency by introducing a communication strategy applicable to any task within a given environment. We pre-train the communication strategy without task-specific reward guidance in a self-supervised manner using a set autoencoder. Our objective is to learn a fixed-size latent Markov state from a variable number of agent observations. Under mild assumptions, we prove that policies using our latent representations are guaranteed to converge, and upper bound the value error introduced by our Markov state approximation. Our method enables seamless adaptation to novel tasks without fine-tuning the communication strategy, gracefully supports scaling to more agents than present during training, and detects out-of-distribution events in an environment. Empirical results on diverse MARL scenarios validate the effectiveness of our approach, surpassing task-specific communication strategies in unseen tasks. Our implementation of this work is available at https://github.com/proroklab/task-agnostic-comms.