A measurement of off-shell Higgs boson production in the ZZ→4ℓ and ZZ→2ℓ2ν decay channels, where ℓ stands for either an electron or a muon, is performed using data from proton–proton collisions at a centre-of-mass energy of s=13 TeV. The data were collected by the ATLAS experiment in 2015 and 2016 at the Large Hadron Collider, and they correspond to an integrated luminosity of 36.1fb−1 . An observed (expected) upper limit on the off-shell Higgs signal strength, defined as the event yield normalised to the Standard Model prediction, of 3.8 (3.4) is obtained at 95% confidence level (CL). Assuming the ratio of the Higgs boson couplings to the Standard Model predictions is independent of the momentum transfer of the Higgs production mechanism considered in the analysis, a combination with the on-shell signal-strength measurements yields an observed (expected) 95% CL upper limit on the Higgs boson total width of 14.4 (15.2) MeV.