A measurement of the t¯t Z and t¯t W production cross sections in final states with either two same-charge muons, or three or four leptons (electrons or muons) is presented. The analysis uses a data sample of proton–proton collisions at √s = 13 TeV recorded with the ATLAS detector at the Large Hadron Collider in 2015, corresponding to a total integrated luminosity of 3.2 fb-1. The inclusive cross sections are extracted using likelihood fits to signal and control regions, resulting in σt¯tZ= 0.9 ± 0.3 pb and σt¯tW= 1.5 ± 0.8 pb, in agreement with the Standard Model predictions.