Nickel is the second most abundant element in the Earth's core. However, the properties of Fe-Ni alloys are still poorly constrained under planetary cores conditions, in particular concerning the effect of Ni on the melting curve of Fe. Here we show that Ni alloying up to 36 wt% does not affect the melting curve of Fe up to 100 GPa. However, Ni strongly modifies the hexagonal-closed-packed/face-centered-cubic (hcp/fcc) phase boundary, pushing the hcp/fcc/liquid triple point of Fe-20wt%Ni to higher pressures and temperatures. Our results allow constraining the triple point for Fe-10wt%Ni, a composition relevant for the Earth interior, and point out a decrease of the melting temperature at core-mantle boundary by 400 K with respect to pure Fe. A lower amount of light elements than previously predicted is thus required to reduce the crystallization temperature of core materials below that of a peridotitic lower mantle, in better agreement with geochemical observations.