  Effects of a flavor singlet vector interaction in the Polyakov - Nambu -
Jona-Lasinio (PNJL) model are studied in combination with the axial U(1)
breaking Kobayashi - Maskawa - 't Hooft interaction. Using a consistent cutoff
scheme we investigate the QCD phase diagram and its dependence on the vector
coupling strength $g_v$. We find that the first order chiral phase transition
at moderate baryon chemical potentials and its critical point, a generic
feature of most NJL-type models without vector coupling, disappear for
sufficiently large values of $g_v$ that are consistent with lattice QCD results
at imaginary chemical potential. The influence of non-zero $g_v$ on the
curvature of the crossover boundary in the $T-\mu$ plane close to $\mu = 0$ is
also examined.
