  Slightly extending a right-handed neutrino version of the $3-3-1$ model, we
show that it is not only possible to solve the strong CP problem but also to
give the total dark matter abundance reported by the Planck collaboration.
Specifically, we consider the possibility of introducing a $3-3-1$ scalar
singlet to implement a gravity stable Peccei-Quinn mechanism in this model.
Remarkably, for allowed regions of the parameter space, the arising axions with
masses $m_a\approx$ meV can both make up the total dark matter relic density
through non-thermal production mechanisms and be very close to the region to be
explored by the IAXO helioscope.
