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While the Hubbard model is the standard model to study Mott metal-insulatortransitions, it is still unclear to which extent it can describemetal-insulator transitions in real solids, where non-local Coulombinteractions are always present. By using a variational principle, we clarifythis issue for short- and long-ranged non-local Coulomb interactions forhalf-filled systems on bipartite lattices. We find that repulsive non-localinteractions generally stabilize the Fermi-liquid regime. The metal-insulatorphase boundary is shifted to larger interaction strengths to leading orderlinearly with non-local interactions. Importantly, non-local interactions canraise the order of the metal-insulator transition. We present a detailedanalysis of how the dimension and geometry of the lattice as well as thetemperature determine the critical non-local interaction leading to afirst-order transition: for systems in more than two dimensions with non-zerodensity of states at the Fermi energy the critical non-local interaction isarbitrarily small; otherwise it is finite.

First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction