The problem of target positions allocation in a formation of autonomous unmanned underwater vehicles (AUVs) under conditions of limited underwater communication is considered. A consensus-based auction algorithm (CBAA) is used to solve this problem, combining decentralized task selection and an assignment approval process between agents. A drawback of classical CBAA is the significant time required to execute multiple consensus phases, especially in an underwater environment where acoustic communication channels are characterized by low bandwidth and significant data transmission delays. A modification of the CBAA is proposed, making it need only a single consensus phase followed by local calculation of the final allocation by each agent based on the full set of bids from all participants. This approach eliminates the need for repeated consensus phases and shifts some of the workload from the communication system to the AUV’s onboard computing system. A comparative analysis of the communication complexity of the original and modified algorithms was conducted. The results confirm the potential of the proposed approach for rapid target positions allocation in large groups of AUVs.