The growth of SrMnO₃ films on SrTiO₃(111) substrates by pulsed laser deposition was studied and found to produce cubic and hexagonal (4H) structures in the SrMnO₃ films. By adjusting the substrate temperature and oxygen pressure, the stability of the two phases was fine-tuned, resulting in the growth of cubic-SrMnO₃(111) or 4H-SrMnO₃(0001) film, with the 4H phase being the more stable at room temperature and ambient pressure in the bulk form. The growth temperature of the cubic phase was also further lowered relative to the bulk thermodynamics by strain at the heterointerface, and once obtained, it was stable at temperatures of up to 800 °C.