We use Monte Carlo simulations and finite-size scaling theory to investigate the phase transition and critical behavior of the S -state block voter model on square lattices. Our numerical results indicate that the system exhibits an order–disorder phase transition at a given value of the noise parameter, which changes from a continuous transition for S ≤ 4 to a discontinuous transition for S ≥ 5 . Moreover, for the cases of continuous transition, the calculated critical exponents indicate that the present studied nonequilibrium model system is in the same universality class of its counterpart equilibrium two-dimensional S -state Potts model. We also provide a first estimation of the long-range exponents governing the dependence on the range of interaction of the magnetization, the susceptibility, and the derivative of Binder’s cumulant.