  We describe an extension of the NuWro Monte Carlo neutrino event generator
with the neutrino-electron scattering processes. This new dynamical channel
includes the charged current and neutral current interactions, together with
their interference, for $\nu_\ell e$ and $\bar\nu_\ell e$ ($\ell=e,\mu,\tau$)
scatterings, resulting in ten possible final states. We illustrate the
performance of the new functionality on few physical examples, including an
estimation of the background in the T2K $\nu_\mu\rightarrow\nu_e$ oscillation
experiment. We show that the background events arising from the
neutrino-electron interactions occupy mostly a distinct region of the phase
space and can be easily separated.
