  We compute the one-loop density power spectrum including Newtonian and
relativistic contributions, as well as the primordial non-Gaussianity
contributions from $f_{\rm NL}$ and $g_{\rm NL}$ in the local configuration. To
this end we take solutions to the Einstein equations in the long-wavelength
approximation and provide expressions for the matter density perturbation at
second and third order. These solutions have shown to be complementary to the
usual Newtonian cosmological perturbations. We confirm a sub-dominant effect
from pure relativistic terms, manifested at scales dominated by cosmic
variance, but find that a sizable effect of order one comes from $g_{\rm NL}$
values allowed by Planck-2018 constraints, manifested at scales probed by
forthcoming galaxy surveys like DESI and Euclid. As a complement, we present
the matter bispectrum at the tree-level including the mentioned contributions.
