  The construction of fractional quantum Hall (FQH) states from the
two-dimensional array of quantum wires provides a useful way to control strong
interactions in microscopic models and has been successfully applied to the
Laughlin, Moore-Read, and Read-Rezayi states. We extend this construction to
the Abelian and non-Abelian $SU(N-1)$-singlet FQH states at filling fraction
$\nu=k(N-1)/[N+k(N-1)m]$ labeled by integers $k$ and $m$, which are potentially
realized in multi-component quantum Hall systems or $SU(N)$ spin systems.
Utilizing the bosonization approach and conformal field theory (CFT), we show
that their bulk quasiparticles and gapless edge excitations are both described
by an $(N-1)$-component free-boson CFT and the $SU(N)_k/[U(1)]^{N-1}$ CFT known
as the Gepner parafermion. Their generalization to different filling fractions
is also proposed. In addition, we argue possible applications of these results
to two kinds of lattice systems: bosons interacting via occupation-dependent
correlated hoppings and an $SU(N)$ Heisenberg model.
