Apical constriction is a major mechanism underlying tissue internalization during development. This cell constriction typically requires actomyosin contractility. Thus, understanding apical constriction requires characterization of the mechanics and regulation of actomyosin assemblies. We have analyzed the relationship between myosin and the polarity regulators Par-6, aPKC and Bazooka (Par-3) (the PAR complex) during amnioserosa apical constriction at Drosophila dorsal closure. The PAR complex and myosin accumulate at the apical surface domain of amnioserosa cells at dorsal closure, the PAR complex forming a patch of puncta and myosin forming an associated network. Genetic interactions indicate that the PAR complex supports myosin activity during dorsal closure, as well as during other steps of embryogenesis. We find that actomyosin contractility in amnioserosa cells is based on the repeated assembly and disassembly of apical actomyosin networks, with each assembly event driving constriction of the apical domain. As the networks assemble they translocate across the apical patch of PAR proteins, which persist at the apical domain. Through loss- and gain-of-function studies, we find that different PAR complex components regulate distinct phases of the actomyosin assembly/disassembly cycle: Bazooka promotes the duration of actomyosin pulses and Par-6/aPKC promotes the lull time between pulses. These results identify the mechanics of actomyosin contractility that drive amnioserosa apical constriction and how specific steps of the contractile mechanism are regulated by the PAR complex.