In the tetragonal heavy fermion system CeCoIn5 the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0–1 GPa) of the basal-plane magnetic penetration depth (λa), the penetration depth anisotropy (γ=λc/λa) and the temperature dependence of 1/λi2 (i=a, c) were studied in single crystals. A strong decrease of λa with pressure was observed, while γ and λi2(0)/λi2(T) are pressure independent. A linear relationship between 1/λa2(270 mK) and Tc was also found. The large decrease of λa with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2.