High-pressure synthesis is a powerful method for the preparation of novel materials with high elastic moduli and hardness. Additionally, such materials may exhibit interesting thermal, optoelectronic, semiconductuing, magnetic or superconducting properties. Here, we report on the high-pressure synthesis of zirconium and hafnium nitrides with the stoichiometry M3N4, where M = Zr, Hf. Synthesis experiments were performed in a laser-heated diamond anvil cell at pressures up to 18 GPa and temperatures up to 3,000 K. We observed formation of cubic Zr3N4 and Hf3N4 (c-M3N4) with a Th3P4-structure, where M-cations are eightfold coordinated by N anions. The c-M3N4 phases are the first binary nitrides with such a high coordination number. Both compounds exhibit high bulk moduli around 250 GPa, which indicates high hardness. Moreover, the new nitrides, c-Zr3N4 and c-Hf3N4 may be the first members of a larger group of,transition metal and/or lanthanide nitrides with interesting ferromagnetic or superconducting behaviour.