A three-dimensional potential energy surface for the ground electronic state of MgH2 has been constructed from 9030 symmetry-unique ab initio points calculated using the icMRCI+Q method with aug-cc-pVnZ basis sets for n=3, 4, and 5, with core-electron correlation calculated at the MR-ACPF level of theory using cc-pCVnZ basis sets, with both calculations being extrapolated to the complete basis set limit. Calculated spectroscopic constants of MgH2 and MgD2 are in excellent agreement with recent experimental results: for four bands of MgH2 and one band of MgD2 the root-mean-square (rms) band origin discrepancies were only 0.44 and 0.06 cm(-1), respectively, and the rms relative discrepancies in the inertial rotational constants (B[v]) were only 0.0196% and 0.0058%, respectively. Spectroscopic constants for MgHD were predicted using the same potential surface.