The position and orientation of the mitotic spindle is precisely regulated to ensure the accurate partition of the cytoplasm between daughter cells and the correct localization of the daughters within growing tissue. Using magnetic tweezers to perturb the position of the spindle in intact cells, we discovered a force-generating machinery that maintains the spindle at the cell center during metaphase and anaphase in one-and two-cell Caenorhabditis elegans embryos. The forces increase with the number of microtubules and are larger in smaller cells. The machinery is rigid enough to suppress thermal fluctuations to ensure precise localization of the mitotic spindle, yet compliant enough to allow molecular force generators to fine-tune the position of the mitotic spindle to facilitate asymmetric division.