A measurement of the top quark-antiquark pair production cross section \(\sigma_{\mathrm{t\overline{t}}}\) 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\(^\pm\mu^\mp\), \(\mu^+\mu^-\), e\(^+\)e\(^-\)) are selected and the cross section is measured from a likelihood fit. For a top quark mass parameter in the simulation of \(m^{\mathrm{MC}}_{\mathrm{t}} =\) 172.5 GeV the fit yields a measured cross section \(\sigma_{\mathrm{t\overline{t}}} =\) 803 \(\pm\) 2 (stat) \(\pm\) 25 (syst) \(\pm\) 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 simulation is performed. The measured value of \(m^{\mathrm{MC}}_{\mathrm{t}} =\) 172.33 \(\pm\) 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.