Transverse momentum spectra of charged pions, kaons, and protons are measured in proton-proton collisions at s=13  TeV with the CMS detector at the LHC. The particles, identified via their energy loss in the silicon tracker, are measured in the transverse momentum range of pT≈0.1–1.7  GeV/c and rapidities |y|<1. The pT spectra and integrated yields are compared to previous results at smaller s and to predictions of Monte Carlo event generators. The average pT increases with particle mass and charged particle multiplicity of the event. Comparisons with previous CMS results at s=0.9, 2.76, and 7 TeV show that the average pT and the ratios of hadron yields feature very similar dependences on the particle multiplicity in the event, independently of the center-of-mass energy of the pp collision.