Using a multiphase transport model, we study the relative importance of J/ψ suppression mechanisms due to plasma screening, gluon scattering, and hadron absorption in heavy ion collisions at the Relativistic Heavy Ion Collider. We find that for collisions between heavy nuclei such as Au+Au, both plasma screening and gluon scattering are important. As a result, the effect due to absorption by hadrons becomes relatively minor. The final J/ψ survival probability in these collisions is only a few percent. In the case of collisions between light nuclei such as S+S, the effect of plasma screening is, however, negligible in spite of the initial high parton density. The final J/ψ survival probability thus remains appreciable after comparable absorption effects due to gluons and hadrons. 25.75.Dw, 24.10.Lx, 24.10.Jv