A new atom-atom interaction potential is introduced for describing by classical molecular dynamics (MD) simulation the physical properties of natural silicate melts. The equation of state, the microscopic structure, the viscosity, the electrical conductivity, and the self-diffusion coefficients of ions in a mid-oceanic ridge basalt (MORB) melt are evaluated by MD over a large range of temperature and pressure (1673-3273 K and 0-60 GPa). A detailed comparison with experimental data shows that the model reproduces the thermodynamic, structural and transport properties of a MORB with an unprecedented accuracy. In particular, it is shown that the MORB melt crystallizes at lower mantle conditions into a perovskite phase whose the equation of state (EOS) is compatible with those proposed in the experimental literature. Moreover, in accordance with experimental findings, the simulation predicts not only that the MORB viscosity exhibits a (slight) minimum with the pressure, but also that the viscosity at high temperature remains very low (<100 mPa.s for T > 2273 K) even at high pressure (up to 40 GPa). However the evolution of the electrical conductivity with temperature and pressure is not always the symmetrical of that of the viscosity. In fact, the relationship between viscosity and electrical conductivity shows a crossover at around 2073 K.