Rapid epithelial tissue flows are essential to building and shaping developing embryos. However, it is not well understood how the mechanical properties of tissues and the forces driving them to flow are jointly regulated to accommodate rapid tissue remodeling. To dissect the roles of actomyosin in the mechanics of epithelial tissue flows, here we use two optogenetic tools, optoGEF and optoGAP, to manipulate Rho/Rho-kinase signaling and actomyosin contractility in the germband epithelium, which flows via convergent extension during Drosophila body axis elongation. The ability to perturb actomyosin across the tissue allows us to analyze the effects of actomyosin on cell rearrangements, tissue tensions, and tissue mechanical properties. We find that either optogenetic activation or deactivation of Rho1 signaling and actomyosin contractility at the apical surface of the germband disrupts cell rearrangements and tissue-level flows. By probing mechanical tensions in the tissue using laser ablation and predicting tissue mechanical properties from cell packings, we find that actomyosin influences both the anisotropic forces driving tissue flow and the mechanical properties of the tissue resisting flow, leading to complex relationships between actomyosin activity and tissue-level flow. Moreover, our results indicate that changes in the distribution of medial and junctional myosin in the different perturbations alter tissue tension and cell packings in distinct ways, revealing how junctional and medial myosin have differential roles in promoting and orienting cell rearrangements to tune tissue flows in developing embryos.