The superfluid density, rho(s), of the iron chalcogenide superconductor, FeSe1-x, was studied as a function of pressure by means of muon-spin rotation. The analysis of rho(s)(T) within the two-gap scheme reveals that the effect on both, the transition temperature T-c and rho(s)(0), is entirely determined by the band(s) where the large superconducting gap develops, while the band(s) with the small gap become practically unaffected.