Animal cells decide where to build the cytokinetic apparatus by sensing the position of the mitotic spindle. Reflecting a long-standing presumption that a furrow-inducing stimulus travels from spindle to cortex via microtubules, debate continues about which microtubules, and in what geometry, are essential for accurate cytokinesis. We used live imaging in urchin and frog embryos to evaluate the relationship between microtubule organization and cytokinetic furrow position. In normal cells, the cytokinetic apparatus forms in a region of lower cortical microtubule density. Remarkably, cells depleted of astral microtubules conduct accurate, complete cytokinesis. Conversely, in anucleate cells, asters alone can support furrow induction without a spindle, but only when sufficiently separated. Ablation of a single centrosome displaces furrows away from the remaining centrosome; ablation of both centrosomes causes broad, inefficient furrowing. We conclude that the asters confer accuracy and precision to a primary furrow-inducing signal that can reach the cell surface from the spindle without transport on microtubules.