A measurement of the top quark-antiquark pair production cross section sigma(t (t) over bar) in proton-proton collisions at a centre-of-mass energy of 13 TeV is presented. The data correspond to an integrated luminosity of 35.9 fb(-1), recorded by the CMS experiment at the CERN LHC in 2016. Dilepton events (e(+/-) mu(-/+), mu(+) mu(-), 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 sigma(t (t) over bar) = 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)(-0.72)(+0.66) (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.