Density-functional theory forces, stresses and energies comprise a database from which the optimal parameters of a spline-based empirical potential combining Stillinger-Weber and modified embeddedatom forms are determined. Accuracy of the potential is demonstrated by calculations of ideal shear, stacking fault, vacancy migration, elastic constants and phonons all between 0 and 100 GPa. Consistency with existing models and experiments is demonstrated by predictions of screw dislocation core structure and deformation twinning in a tungsten nanorod. Lastly, the potential is used to study the stabilization of fcc tungsten at high pressure.