A measurement of the tt¯Z and tt¯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 σtt¯Z=0.9±0.3 pb and σtt¯W=1.5±0.8 pb, in agreement with the Standard Model predictions.