To ensure timely cytokinesis, the equatorial actomyosin contractile ring constricts at a relatively constant rate despite its progressively decreasing size. Thus, the per-unit-length constriction rate increases as ring perimeter decreases. To understand this acceleration, we monitored cortical surface and ring component dynamics during the first cytokinesis of the Caenorhabditis elegans embryo. We found that, per unit length, the amount of ring components (myosin, anillin) and the constriction rate increase with parallel exponential kinetics. Quantitative analysis of cortical flow indicated that the cortex within the ring is compressed along the axis perpendicular to the ring, and the per-unit-length rate of cortical compression increases during constriction in proportion to ring myosin. We propose that positive feedback between ring myosin and compression-driven flow of cortex into the ring drives an exponential increase in the per-unit-length amount of ring myosin to maintain a high ring constriction rate and support this proposal with an analytical mathematical model.