A fundamental step in many bioinformatics computations is to count the frequency of fixed-length sequences, called k-mers, a problem that has received considerable attention as an important target for shared memory parallelization. With datasets growing at an exponential rate, distributed memory parallelization is becoming increasingly critical. Existing distributed memory k-mer counters do not take advantage of GPUs for accelerating computations. Additionally, they do not employ domain-specific optimizations to reduce communication volume in a distributed environment. In this paper, we present the first GPU-accelerated distributed-memory parallel k-mer counter. We evaluate the communication volume as the major bottleneck in scaling k-mer counting to multiple GPU-equipped compute nodes and implement a supermer-based optimization to reduce the communication volume and to enhance scalability. Our empirical analysis examines the balance of communication to computation on a state-of-the-art system, the Summit supercomputer at Oak Ridge National Lab. Results show overall speedups of up to two orders of magnitude with GPU optimization over CPU-based k mer counters. Furthermore, we show an additional 1.5× speedup using the supermer-based communication optimization.