Seismological data can yield physical properties of the Earth's core, such as its size and seismic anisotropy1,2,3. A well-constrained iron phase diagram, however, is essential to determine the temperatures at core boundaries and the crystal structure of the solid inner core. To date, the iron phase diagram at high pressure has been investigated experimentally through both laser-heated diamond-anvil cell and shock-compression techniques, as well as through theoretical calculations4,5,6,7,8,9,10,11,12,13,14,15,16,17. Despite these contributions, a consensus on the melt line or the high-pressure, high-temperature phase of iron is lacking. Here we report new and re-analysed sound velocity measurements of shock-compressed iron at Earth-core conditions15. We show that melting starts at 225 ± 3 GPa (5,100 ± 500 K) and is complete at 260 ± 3 GPa (6,100 ± 500 K), both on the Hugoniot curve—the locus of shock-compressed states. This new melting pressure is lower than previously reported16, and we find no evidence for a previously reported solid–solid phase transition on the Hugoniot curve near 200 GPa (ref. 16).