By using the modified method of the Fermi pseudopotential and the effective Hamiltonian method, a multiconfiguration calculation of the potential curves is performed for the Hg(6 ^1,3P_J) + He and Hg(7 ^1,3S_J) + He interactions in the region of interatomic separations R ≥ 5a₀. In this calculation, the interactions of different excited configurations and the spin-orbit coupling of singlet and triplet states were taken into account. The Hg⁺ + He ion-atom interaction potential was obtained by the nonempirical configuration interaction method MRD-CI with the use of the relativistic effective core potential (RECP) for the Hg atom. Based on the calculated potential curves and the transition dipole moments, the process of radiative decay of the Hg(6 ³P₂) metastable state in collisions with He atoms is considered and the temperature dependence of the rate constant is calculated.