This paper describes a measurement of the inclusive top quark pair production
cross-section ($\sigma_{t\bar{t}}$) with a data sample of 3.2 fb$^{-1}$ of
proton--proton collisions at a centre-of-mass energy of $\sqrt{s}$=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 $\sigma_{t\bar{t}}$ 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:
$\sigma_{t\bar{t}}$= 818 $\pm$ 8 (stat) $\pm$ 27 (syst) $\pm$ 19 (lumi) $\pm$
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.