A search is presented for new physics in events with two low-momentum, oppositely charged leptons (electrons or muons) and missing transverse momentum in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data collected using the CMS detector at the LHC correspond to an integrated luminosity of 35.9. The observed event yields are consistent with the expectations from the standard model. The results are interpreted in terms of pair production of charginos and neutralinos ( and ) with nearly degenerate masses, as expected in natural supersymmetry models with light higgsinos, as well as in terms of the pair production of top squarks ( ), when the lightest neutralino and the top squark have similar masses. At 95% confidence level, wino-like masses are excluded up to 230 GeV for a mass difference of 20 GeV relative to the lightest neutralino. In the higgsino-like model, masses are excluded up to 168 GeV for the same mass difference. For pair production, top squark masses up to 450 GeV are excluded for a mass difference of 40 GeV relative to the lightest neutralino.