A family of interatomic potentials is constructed for which the intrinsic ductility can be tuned systematically. Specifically, the elastic constants and critical energy release rate for Griffith cleavage, G(Ic), are held constant, while the critical energy release rate for dislocation emission, G(Ie), can be varied. This behavior is achieved by modifying a standard near-neighbor pair potential; the new potential is applicable to either 2D (hexagonal lattice) or 3D (FCC/HCP). Analytical expressions are provided for GIe and GIc, enabling a potential with a desired intrinsic ductility to be easily developed. Direct atomistic simulations are used to demonstrate that the new potentials control the intrinsic material ductility, i.e. crack tip dislocation emission versus brittle cleavage, under quasi-static loading. For the 2D potential, the mode I crack tip behavior can be tuned from brittle to ductile; for the 3D potential, such tuning is only possible for certain crack orientations. More generally, the new potentials are expected to be useful in a wide range of physical problems in which behavior is controlled by the ability of the material to nucleate dislocations, including problems involving crack tips, grain boundaries, contact and friction, and bi-material interfaces.