While low-temperature relaxations show significant differences among metallic glasses with different compositions, the underlying mechanism remains mysterious. Using molecular dynamics simulation, low-temperature relaxation of amorphous solids is investigated in model systems with different atomic interaction stiffness. It was found that as the interaction stiffness increases, the low-temperature relaxation is enhanced. The fraction of mobile atoms increases with increasing interaction stiffness, while the length scale of dynamical heterogeneity does not change. The enhanced relaxation may be due to increased dynamical heterogeneity. These findings provide a physical picture for better understanding the origin of low-temperature relaxation dynamics in amorphous solids, and the experimentally observed different β-relaxation behaviors in various metallic glasses.