A search for supersymmetry in events with two or three low-momentum leptons and missing transverse momentum is performed. The search uses proton-proton collisions at s = 13 TeV collected in the three-year period 2016–2018 by the CMS experiment at the LHC and corresponding to an integrated luminosity of up to 137 fb−1. The data are found to be in agreement with expectations from standard model processes. The results are interpreted in terms of electroweakino and top squark pair production with a small mass difference between the produced supersymmetric particles and the lightest neutralino. For the electroweakino interpretation, two simplified models are used, a wino-bino model and a higgsino model. Exclusion limits at 95% confidence level are set on χ~20/χ~1± masses up to 275 GeV for a mass difference of 10 GeV in the wino-bino case, and up to 205(150) GeV for a mass difference of 7.5 (3) GeV in the higgsino case. The results for the higgsino are further interpreted using a phenomenological minimal supersymmetric standard model, excluding the higgsino mass parameter μ up to 180 GeV with the bino mass parameter M1 at 800 GeV. In the top squark interpretation, exclusion limits are set at top squark masses up to 540 GeV for four-body top squark decays and up to 480 GeV for chargino-mediated decays with a mass difference of 30 GeV. [Figure not available: see fulltext.].