We have used x-ray diffraction to determine the structure factor of water along its melting line to a static pressure of 57 GPa (570 kbar) and a temperature of more than 1500 K, conditions which correspond to the lower mantle of the Earth, and the interiors of Neptune and Uranus up to a depth of 7000 km. We have also performed corresponding first principles and classical molecular dynamics simulations. Above a pressure of 4 GPa the O-O structure factor is found to be very close to that of a simple soft sphere liquid, thus permitting us to determine the density of liquid water near the melting line. By comparing these results with the density of ice, also determined in this study, we find that the enthalpy of fusion (DeltaH(f)) increases enormously along the melting line, reaching approximately 120 kJ/mole at 40 GPa (compared to 6 kJ/mole at 0 GPa), thus revealing significant molecular dissociation of water upon melting. We speculate that an extended two-phase region could occur in planetary processes involving the adiabatic compression of water.