Context. Maser lines from different molecular species, including water, hydroxyl, and methanol, are common observational phenomena associated with massive star-forming regions. In particular, since its discovery, the 6.7 GHz methanol maser has been recognized as one of the clearest signposts in the formation of young high-mass stars. Aims. The methanol maser thus appears as an ideal tool for studying the early phases of massive star formation. However, it is difficult to establish the exact start of the methanol maser phase, and it would then be interesting to detect and study low flux-density methanol masers (i.e., 0.1 Jy or even 0.1 Jy), in order to determine if they can be used effectively to mark a specific evolutionary phase in high-mass star formation. Methods. Past surveys have been unable to systematically detect many low flux-density methanol masers, and thus we do not yet know how many such masers exist in the Galaxy and what their physical nature is. A large sample of massive cores can now be found in the Herschel infrared GALactic Plane Survey (Hi-GAL), which we have used to search for methanol and excited OH masers toward a sample of starless and protostellar high-mass clumps using the Arecibo telescope. Results. Out of a sample of 107 observed Hi-GAL sources, we detected a total of 37 methanol masers, with 22 sources being new and weak (median peak flux density 0.07 Jy) detections, in the Galactic longitude range [32. ◦0, 59. ◦8]. We also detected 12 6.035 GHz OH maser regions, with 9 new detections. Our survey covers a similar range of source distances to the “Arecibo Methanol Maser Galactic Plane Survey” (or AMGPS, Pandian et al. 2007), but the methanol masers detected by us are clearly shifted toward lower integrated flux densities. Conclusions. The newly detected methanol masers mostly have low luminosity (assuming isotropic emission), and except for some sources, their weakness is not due to distance effects or positional offsets. No specific correlation is found with the physical parameters of the Hi-GAL clumps, except for sources with both CH3OH and OH masers, which tend to have higher mass and luminosity. The intensity of the methanol masers correlates well with the velocity range of the maser emission, which suggests that the low brightness of these masers is related to the number of maser spots in the emitting region and to their evolution with time.
