  We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$
supersymmetric gauge theories regularized by higher covariant derivatives
produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This
is done using a recently proposed algorithm, which essentially simplifies such
multiloop calculations. The result is presented in the form of an integral of
double total derivatives in the momentum space. The considered contribution to
the $\beta$-function is compared with the two-loop anomalous dimension of the
Faddeev--Popov ghosts. This allows verifying the validity of the NSVZ equation
written as a relation between the $\beta$-function and the anomalous dimensions
of the quantum superfields. It is demonstrated that in the considered
approximation the NSVZ equation is satisfied for the renormalization group
functions defined in terms of the bare couplings. The necessity of the
nonlinear renormalization for the quantum gauge superfield is also confirmed.
