  We adapt the type II seesaw mechanism to the framework of the 3-3-1 model
with right-handed neutrinos. We emphasize that the mechanism is capable of
generating small masses for the left-handed and right-handed neutrinos and the
structure of the model allows that both masses arise from the same Yukawa
coupling. For typical values of the free parameters of the model we may obtain
at least one right-handed neutrino with mass in the KeV range. Right-handed
neutrino with mass in this range is a viable candidate for the warm component
of the dark matter existent in the universe.
