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 (lambda_a), the penetration depth anisotropy (gamma=lambda_c/lambda_a) and the temperature dependence of 1/lambda_i^2 (i=a,c) were studied in single crystals. A strong decrease of lambda_a with pressure was observed, while gamma and lambda_i^2(0)/lambda_i^2(T) are pressure independent. A linear relationship between 1/lambda_a^2(270 mK) and Tc was also found. The large decrease of lambda_a with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2.