A bstract 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 corresponding to an integrated luminosity of 139 fb − 1 is presented. Events are selected if they contain a single lepton (electron or muon) or an opposite-sign lepton pair, in association with multiple jets. The events are categorised according to the number of jets and how likely these are to contain b -hadrons. A multivariate technique is then used to discriminate between signal and background events. The measured four-top-quark production cross section is found to be $$ {26}_{-15}^{+17} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mn>26</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>15</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> 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 $$ {24}_{-6}^{+7} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mn>24</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> fb, with a corresponding observed (expected) signal significance of 4.7 (2.6) standard deviations over the background-only predictions. It is consistent within 2.0 standard deviations with the Standard Model expectation of 12 . 0 ± 2 . 4 fb.