Actomyosin contractility underlies force generation in morphogenesis ranging from cytokinesis to epithelial extension or invagination. In Drosophila, the cleavage of the syncytial blastoderm is initiated by an actomyosin network at the base of membrane furrows that invaginate from the surface of the embryo. It remains unclear how this network forms and how it affects tissue mechanics. Here, we show that during Drosophila cleavage, myosin recruitment to the cleavage furrows proceeds in temporally distinct phases of tension-driven cortical flow and direct recruitment, regulated by different zygotic genes. We identify the gene dunk, which we show is transiently transcribed when cellularization starts and functions to maintain cortical myosin during the flow phase. The subsequent direct myosin recruitment, however, is Dunk-independent but requires Slam. The Slam-dependent direct recruitment of myosin is sufficient to drive cleavage in the dunk mutant, and the subsequent development of the mutant is normal. In the dunk mutant, cortical myosin loss triggers misdirected flow and disrupts the hexagonal packing of the ingressing furrows. Computer simulation coupled with laser ablation suggests that Dunk-dependent maintenance of cortical myosin enables mechanical tension build-up, thereby providing a mechanism to guide myosin flow and define the hexagonal symmetry of the furrows.