Variations of the mass-independent abundance of Mg-26 (delta Mg-26*) and stable Mg ((delta Mg-25) isotope composition of chondrites are important because they constrain the homogeneity of Al-26 and Mg isotopes in the proto-planetary disc and the validity of the short-lived Al-26-to-Mg-26 chronometer applied to meteorites. We present high-precision Mg isotope data and Al/Mg ratios of chondrites representing nearly all major chondrite classes, including a step-leaching experiment on the CM2 chondrite Murchison. delta Mg-26* variations in leachates of Murchison representing acid soluble material are <= 30 times smaller than reported for neutron-rich isotopes of Ti and Cr and do not reveal resolvable deficits in delta Mg-26* (-0.002 to +0.118 parts per thousand). Very small variations in delta Mg-26* anomalies in bulk chondrites (-0.006 to +0.019 parts per thousand) correlate with increasing Al-27/Mg-24 ratios and delta Ti-50, reflecting the variable presence of calcium-aluminium-rich inclusions (CAls) in some types of carbonaceous chondrites. Similarly, release of radiogenic Mg-26 produced by Al-26 decay from CAl material in the step-leaching of Murchison best explains the high delta Mg-26* observed in the last, aggressive, leaching steps of this experiment. Overall, the observed variations in delta Mg-26* are small and potential differences beyond that which result from the presence of CAl-like material cannot be detected within the analytical uncertainties of this study (+/- 0.004 parts per thousand). The results do not allow radical heterogeneity of Al-26 (>=+/- 30%) or measurable Mg nucleosynthetic heterogeneity (>=+/- 0.005 parts per thousand) to have existed on a planetesimal scale in the proto-planetary disc. Combined with published delta Mg-26* data for CAls, the bulk chondrite data yield a precise initial (Al-26/Al-27)(0) = (5.21 +/- 0.06) x 10(-5) and delta Mg-26* = -0.0340 +/- 0.0016 parts per thousand for the Solar System. However, it is not possible with the currently available data to determine with certainty whether CAls and the material from which planetesimals accreted including chondrite parent bodies had precisely the same initial levels of Al-26, although planetesimals and planets appear to have accreted from material with a mean initial (Al-26/Al-27)(0) in the range of 2.1 to 6,7x 10(-5). The average stable Mg isotope composition of all analysed chondrites, with the exception of a chondrule from the CBa chondrite Gujba (delta Mg-25(DSM-3) = 0.032 +/- 0.035 parts per thousand), is delta Mg-25(DSM-3) = -0.152 +/- 0.079 parts per thousand (2 sd) and is indistinguishable from that of the Earth's mantle. (C) 2010 Elsevier B.V. All rights reserved.