The current view of structural relaxation in metallic glasses assumes the presence of primary and secondary processes with different activation energies. While the faster, secondary process can be well characterized in the out-of-equilibrium state below the glass transition temperature Tg, the experimental direct determination of the primary process in this temperature region is more difficult due to the long relaxation times. In this work, we merge new and literature data to analyze the temperature behavior of the primary relaxation time below Tg as observed by mechanical spectroscopy and stress relaxation of metallic glasses of different fragility. We compare these results with the microscopic structural relaxation times previously measured with X-ray photon correlation spectroscopy. The coincidence between the macroscopic and microscopic relaxation times allows us to discuss the underlying mechanisms responsible of primary relaxation over different length scales, as well as to propose an overall picture of the primary relaxation behavior in the glassy regime near Tg.