This is a tungsten-rhenium (W-Re) classical interatomic potential developed within the embedded atom method interaction framework. A force-matching method was employed to fit the potential to ab initio forces, energies, and stresses. Simulated annealing was combined with the conjugate gradient technique to search for an optimum potential from over 1000 initial trial sets. The potential is designed for studying point defects in W-Re systems. It gives good predictions of the formation energies of Re defects in W and the binding energies of W self-interstitial clusters with Re. In pure Re, the potential can reproduce the formation energies of vacancies and self-interstitial defects sufficiently accurately and gives the correct ground state self-interstitial configuration. Liquid structures were included in the fit, ensuring that the potential yields a Re melting temperature (3130 K) that is close to the experimental value (3459 K).