We report an experimental and theoretical study of the phase diffusion in small Josephson junctions under microwave irradiation. A peculiar enhancement of the phase diffusion by microwaves is observed. The enhancement manifests itself by a pronounced current peak in the current-voltage characteristics. The voltage position V(top) of the peak increases with the power P of microwave radiation as V(top) proportional to sqrt[P], while its current amplitude weakly decreases with P. As the microwave frequency increases, the peak feature evolves into Shapiro steps with a finite slope. Our theoretical analysis, taking into account the enhancement of incoherent superconducting current by multiphoton absorption, is in good agreement with experimental data.