A measurement of the top quark–antiquark pair production cross section σ_tt¯ 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 m_t^MC = 172.5 GeV the fit yields a measured cross section σ_tt¯ = 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 m_t^MC = 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.