Using a nonlocal version of the Polyakov-loop-extended Nambu-Jona-Lasinio model, we investigate effects of a nonderivative vector-current interaction (relating to the quark-number density) at both real and imaginary chemical potentials. This repulsive vector interaction between quarks has the following impact on the chiral first-order phase transition: at imaginary chemical potential it sharpens the transition at the Roberge-Weiss (RW) end point and moves this critical point toward lower temperatures; at real chemical potential, the critical end point moves on a trajectory towards larger chemical potentials and lower temperatures with increasing vector coupling strength. The conditions are discussed at which the first-order phase transition disappears and turns into a smooth crossover.