Abstract: This paper describes a measurement of the inclusive top quark pair production cross-section (sigma(t (t) over bar)) with a data sample of 3.2 fb(-1) of proton-proton collisions at a centre-of-mass energy of root s = 13 TeV, collected in 2015 by the ATLAS detector at the LHC. This measurement uses events with an opposite-charge electron-muon pair in the final state. Jets containing b-quarks are tagged using an algorithm based on track impact parameters and reconstructed secondary vertices. The numbers of events with exactly one and exactly two b-tagged jets are counted and used to determine simultaneously sigma(t (t) over bar) and the efficiency to reconstruct and b-tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section is measured to be: s(t (t) over bar)= 818 +/- 8 (stat) +/- 27 (syst) +/- 19 (lumi) +/- 12 (beam) pb, where the four uncertainties arise from data statistics, experimental and theoretical systematic effects, the integrated luminosity and the LHC beam energy, giving a total relative uncertainty of 4.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. A fiducial measurement corresponding to the experimental acceptance of the leptons is also presented.