We have investigated phase relations and melting behavior of Fe3C and Fe7C3 using X-ray diffraction in a laser-heated diamond cell up to 185 GPa and 5200 K. Our results show that the starting Fe3C sample decomposes into a mixture of solid orthorhombic Fe7C3 and hcp-Fe at above 145 GPa upon laser heating and then transforms into Fe-C liquid and solid Fe7C3 at temperatures above 3400 K. Using the intensity of the diffuse scattering as a primary criteria for detecting melting, the experimentally derived liquidus for a bulk composition of Fe3C fitted with the Simon-Glatzel equation is T-m(K) = 1800 x [1 + (P-m = 5.7)/15.10 +/- 2.55](1/2.41) (+/- 0.17) at 24-185 GPa, which is similar to 500 K higher than the melting curve of iron reported by Anzellini et al. (2013) at Earth's core pressures. The higher melting point and relative stability of Fe7C3 in Fe-rich Fe-C system at Earth's core conditions indicate that Fe7C3 could solidify out of the early Earth's molten core to become a constituent of the innermost inner core.