We investigate the current-phase relation (CPR) of long diffusive superconductor-normal-metal-superconductor (Nb/Ag/Nb) Josephson junctions in thermodynamic equilibrium and under microwave irradiation. While in equilibrium good agreement with the predictions of quasiclassical theory is found, we observe that the shape of the CPR can be strongly affected by microwave irradiation. Close to a Josephson-phase difference phi similar or equal to pi, the supercurrent can be strongly suppressed when increasing the rf power. Our results can be understood in terms of microwave excitation of low-lying Andreev bound states across the minigap in the junction. In the frequency interval studied, this mechanism becomes important, when the minigap closes at phi similar or equal to pi.