The effect of added salt (NaCl) on the melting of ice is studied using molecular dynamics simulations. The equilibrium freezing point depression observed in the simulations is in good agreement with experimental data. The kinetic aspects of melting are investigated in terms of the exchange of water molecules between ice and the liquid phase. The ice/liquid equilibrium is a highly dynamic process with frequent exchange of water molecules between ice and the liquid phase. The balance is disturbed when ice melts and the melting proceeds in two stages; the inhibition of the association of water molecules to the ice surface at short times, followed by the increased dissociation of water molecules from the ice surface at longer times. We also find that Cl- ions penetrate more deeply into the interfacial region than Na+ ions during melting. This study provides an understanding of the kinetic aspects of melting that could be useful in other processes such as the inhibition of ice growth by antifreeze proteins.