To investigate the nebular history of material contributing to the terrestrial planets, and search for evidence of a high-temperature origin of the Moon, we measured Mg isotopic compositions of primitive olivines from the Earth, Moon, Mars, and pallasite parent body using laser-ablation multi-collector ICPMS. No temporal variation in the Earth's mantle since at least 3.8 Ga, and only limited variations in the compositions of mantle sources from diverse tectonic settings were found. Earth, Moon, Mars, and differentiated asteroids appear to have formed from a nebular reservoir that was homogeneous with respect to Mg isotopes. This implies either a minor role for evaporation-condensation in the inner solar system, or a limited variation in the proportion of refractory CAI-like material contributing to the terrestrial planets. The Mg isotopic composition of the Moon is identical to the Earth's mantle, placing strong constraints on any volatility-related fractionation that occurred during formation of the Moon.