A measurement of the top quark–antiquark pair production cross section σtt¯ in proton–proton collisions at a centre-of-mass energy of 13 TeV is presented. The data correspond to an integrated luminosity of 35.9fb−1 , recorded by the CMS experiment at the CERN LHC in 2016. Dilepton events ( e ± μ ∓ , μ+μ− , e+e− ) are selected and the cross section is measured from a likelihood fit. For a top quark mass parameter in the simulation of mMCt=172.5GeV the fit yields a measured cross section σtt¯=803±2(stat)±25(syst)±20(lumi)pb , in agreement with the expectation from the standard model calculation at next-to-next-to-leading order. A simultaneous fit of the cross section and the top quark mass parameter in the powheg simulation is performed. The measured value of mMCt=172.33±0.14(stat)+0.66−0.72(syst)GeV is in good agreement with previous measurements. The resulting cross section is used, together with the theoretical prediction, to determine the top quark mass and to extract a value of the strong coupling constant with different sets of parton distribution functions.