We consider the generation of a quasistatic longitudinal electric field by intense laser pulses propagating in a transparent plasma with radiation friction (RF) taken into account. For both circular and linear polarization of the driving pulse we develop a 1D analytical model of the process, which is valid in a wide range of laser and plasma parameters. We define the parameter region where RF results in an essential enhancement of the longitudinal field. The amplitude and the period of the generated longitudinal wave are estimated and optimized. Our theoretical predictions are confirmed by 1D and 2D PIC simulations. We also demonstrate numerically that RF should substantially enhance the longitudinal field generated in a plasma by a 10 PW laser such as ELI Beamlines.