A measurement of four-top-quark production using proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the ATLAS detector at the Large Hadron Collider with an integrated luminosity of 139/fb is presented. A new result uses events with a single lepton (electron or muon) or an opposite-sign lepton pair, in association with multiple jets. The measured four-top-quark production cross section is found to be 26 +17 -15 fb, with a corresponding observed (expected) significance of 1.9 (1.0) standard deviations over the background-only hypothesis. The result is combined with the previous measurement performed by the ATLAS Collaboration in the multilepton final state. The combined four-top-quark production cross section is measured to be 25 +7 -6 fb, with a corresponding observed (expected) signal significance of 4.7 (2.6) standard deviations over the background-only predictions. The result is consistent within 2.0 standard deviations with the Standard Model expectation of 12.0 +/- 2.4 fb.